Shapeless—a new language concept and related technology

ABSTRACT

Shape Dependent alphabets are error prone and quite imposing on their reader. Proposing “Shapeless”—an alphabet based on the entropic state of a mixture—offering easy, redundant reading. Applications include marking packages for shipping and industrial handling, signing items to hinder fraud, offering alternative communication channels, and analyzing video streams for changes of interest.

US PATENT APPLICATION SPECIFICATIONS

Shape Dependent alphabets are error prone and quite imposing on theirreader. Proposing Shapeless—an alphabet based on the entropic state of amixture—offering easy, redundant reading. Applications include markingpackages for shipping and industrial handling, signing items to hinderfraud, offering alternative communication channels, and analyzing videostreams for changes of interest.

CROSS REFERENCE TO RELATED APPLICATIONS

Provisional Application No. 63/051,652 filed on Jul. 14, 2020;Provisional Application No. 63/034,401 filed on Jun. 4, 2020;Provisional Application No. 63/005,062 filed on Apr. 3, 2020;Provisional Application No. 62/963,855 filed on Jan. 21, 2020;Provisional Application No. 62/931,807 filed on Nov. 7, 2019;Provisional Application No. 62/926,560 filed on Oct. 27, 2019;Provisional Application No. 62/900,567 filed on Sep. 15, 2019.”

BACKGROUND OF THE INVENTION

Computer technology opened an array of possibilities for new and usefullanguages, helping in human interaction and supporting man-machineinterface. E.g.: Base64, barcodes, QR, emoji. At the human end all theselanguages have shape-based letters. To be read right these shapes needto be viewed from a certain direction (to prevent confusion like between“6” and “9”), and the full geometry of the letters must be readable (Sothat an “E” is not interpreted as an “F”). This background ofshape-based alphabet suggests a conceptual departure towards a‘shapeless alphabet’ where information is captured not by thespecificity of shape, form and geometry, but otherwise, particularlythrough the degree of entropy expressed in a mixture of two ingredients.The human eye distinguishes between uniform and less uniform mixtures,and a camera will do so very well. Historically, new languages openeddoors to important new developments; one may expect a similar outcomehere.

BRIEF SUMMARY OF THE INVENTION

Language is traditionally written with shape-based letters, as English,or bar-codes, or even emoji icons. Reading such letters may be easilydistorted if a line or two are missing or folded. This inventiondescribes a language written with shapeless entities, namely the lettersdo not depend on specific shape and form, but rather on quantitativeratio between two mixed ingredients, and the degree of uniformity oftheir mixture. The “shapeless” letter (also known as the entropicletter) can be accurately read from any direction over a folded orcurved surface where some parts are covered, allowing for robust messagewriting. Applications include packaging, shipping, handling, industrialcontrol, preventing friendly fire, emergency rescue, and various videotechnology applications. The invention describes shapeless lettersgenerated on computer screens and shapeless letters generated through aninvented entropic mixer, mixing two chemicals into a mixturerepresenting an entropic message.

BRIEF EXPLANATION OF DRAWINGS

FIG. 1 Entropic Reading Illustration The figures shows a boardconstructed from 4×4=16 squares which are marked as either ingredient A(shaded squares) or ingredient B, (unshaded squares). Two entropic modesare shown: (i) the A squares come in chunks of 4 contingent squares,(ii) the A squares come in individual squares. The board is analyzedthrough 10 randomized slicing. Each slice is analyzed per its A v. Bcontents, and the results are computed in the section “illustration” inthe specifications. Three sizes of slices are used: 4, 6, and 8 squares.In each of the slice sizes, the result show that the entropy (theuniformity) is higher in the case where ingredient A is distributed perindividual squares, as expected.

FIG. 2 Entropic Mixing Apparatus This figure shows a basic bilateralapparatus. Two ingredients A and B are pushed from below, each with itsown pressure P_(a) and P_(b) respectively. The two ingredients are fedinto the entropic mixer, EM where they are mixed in a desired state ofentropy and pumped on from there. The EM is controlled by an electroniccontroller, C.

FIG. 3 Multi Ingredient Entropic Mixer This figure shows an entropicmixer taking in 4 ingredients A, B, C, and D. The ingredients are fedinto the EM, which arranges them in the desired entropic state.Similarly there may be any number of ingredients entropically mixed.

FIG. 4: Cascaded Entropic Mixing Apparatus This figure show a 4ingredient mixing apparatus fed with the output of four bilateralentropic mixtures, so that all in all 8 ingredients build up theentropic state (A, B, C, D, E, F, G, H). This configuration maintainsthe bilateral entropic message between the ingredients in the bilateralmixers, namely A v. B, C. v. D. E v. F and G v. H.

FIG. 5: Entropic Mixing Stages This figure shows how two ingredients arefed into an entropic mixing apparatus. They first encounter a stationarydisk “S” fitted with holes of desired size through which the twoingredients flow further as the upper disc, “R” rotates at a desiredspeed, and every round it ‘chops’ a chunk of both ingredients, sendingthem to the next stage—the mixing stage where two discs, “U” and “V” arerotating in counter directions and each at desired speed, so that theycreate a moving location for the opening through which the mixture ismoving to the next stage where again two discs “G” and “H” also rotatein counter directions, similarly create a moving location for the flowemergence forward. Such sets of two rotating discs may be added at will.Eventually the mixture emerges from the contraption with a desiredentropic state.

FIG. 6 Entropic Ratio Disc Set This figure shows flat view of the twodiscs marked “S” and “R” shown in future 5, only that in this figure thediscs are set to admit 6 ingredients to be co-mixed entropically. Thefigure shows disc S with 6 holes of varying sizes. Each hole will be fedby a supply line of one ingredient. Disc R rotates abreast of disc S.Every time the disk R opening overlaps over a given opening in disc Sthe ingredient that flows through this hole is admitted to the nextentropic chamber. The faster R rotates the less ingredient material isadmitted. The larger the hole for the ingredient, the more of theingredient is admitted. The greater the pressure that the ingredient isunder, the more ingredient material is pushed through.

FIG. 7 Slicing Round of a Three Ingredients Entropic Mixing This figureshows a stationary entropic ring with three different size holes. Eachhole is shown to be the terminal point of a feeding line of aningredient destined for entropic mixing. (Shown in blue, pink, andblack). The figure shows above the disc a graphics of the column ofmaterial of each ingredient that is cooped up in one round of disc Rthat rotates abreast of disc S. The ingredient with the larger hole, ispumped in in a greater amount. The exact amount pumped for the mixingalso depends on the pressure that moves each ingredient and therespective viscosity thereto. Disc R is shown in the Sid. The figureshows how the ‘sliced columns’ of ingredients are pushed to the mixingset of disc, which like in FIG. 5 is comprised of two moving discsrotating counter each other, creating a moving spot for the flowforward.

FIG. 8 Entropic Ratio Discs This figure shows two types of stationarydiscs in an entropic mixture setup. The top one admits up to 5ingredients, each admitted through the same size opening. The bottomdisc is fitted with 8 holes of different aperture size each, admittingup to 8 ingredients to be entropically mixed.

FIG. 9: Entropic Marking with Tracers This figure shows two entropicingredients symbolized by squares and circles, as they are fed into anentropic mixer which in turn injects the mix into a carrier fluid.

FIG. 10 Variable Aperture ENtropic Disc This figure shows a stationaryentropic disc fitted with three inlet holes, where each inlet hole isbuilt as a variable aperture contraption so that the entropic mixercontroller can set the size of the hole for each mixing batch.

FIG. 11 Entropic Message is Inherent The figure shows a block of matterconstructed with an entropic message, which is visible from anydirection through any face of the block, and when the block is cut—themessage is readable from the faces that were exposed in the cut.

FIG. 12 Entropic Message Readable on a tall flag on a windy day Thefigure shows a flag flapping in a strong wind. Any shape-wise languageon it will be hard to read, but an entropic message is easily readable.Important in cases of emergency.

FIG. 13: Entropic Reader Monitors Dispensing of Pills The figure shows apill dispensing tray with entropically marked pills which are monitoredby a fixed entropic reader. The figures shows several sorts of pillsentropically marked. Such marking can be used together with shapeinformation to monitor handling of pills.

FIG. 14 Preventing Friendly fire with Entropically Marked uniformFriendly fire is a painful unresolved problem in the battlefield.Machinegun and rifles can be fitted with an entropic reader that willidentify friendly uniform even is dusty and only partially exposed, andthen either not shoot or alert the shooter. It is difficult to achievethis degree of field efficacy with shape based alphabet.

FIG. 15 Entropic Writer This figure depicts a hand-held entropic writer,fed from two containers with the mixed ingredients. It spray-paints anentropic layer on some surface, ready for an entropic reader to read.

FIG. 16 Entropically Marked Rolling Balls The figure shows rails overwhich balls are rolling down the slope. When a ball drops from the railto the next station of its processing, it is viewed by two entropicreaders that keep track of which ball came through. The balls can beobjects of interests or they may be handling enclosures housing someitems of interest. The advantage of balls is that they roll freely onevery minor slope and which is easier and cheaper to install thanrolling conveyors needed for square boxes. Since the entropic message isreadable from every direction, it makes no difference if the ballrotates. By contrast any shape based alphabet require particularorientation between the reader and the examined object.

FIG. 17: Entropic Mixing Apparatus (EMA) configuration. This figureshows the configuration of the apparatus, EMA. The two mixed ingredientsA and B are fed into the EM—the entropic mixer. The stream is controlledthrough valves, which in turn are controlled by the entropic mixercontroller, EMC. The EMC also controls various operational parameters ofthe EM, as shown with four dotted lines. The mixture generated in the EMflows out, as shown in the solid arrow marked by “M” (mixture). As itcomes out the mixture is examined by an entropic reader that is part ofthe EM apparatus. The mixture readings are routed back to the EMcontroller. The logic inside the controller adjusts the controlledparameters to bring the output closer to the desired entropic message itshould carry. This desired message is inputted to the EMC through anoutside line marked entropic set point (esp). Standard controlalgorithms are employed in the EMC to adjust the output until it fitsthe desired set point. The EMA also includes the option to injectdivider material to the mix, to signal the boundaries where the mixturecarries the desired message, and to indicate boundaries betweenindividual messages (letters) which combine into words. The EMA may beequipped with a heater or a cooler as the case may be, to adjust theviscosities of ingredients A and B to the desired range. Heat generallylower viscosities, and cold temperature increases them. But there areexceptions. These heat exchangers may be fitted on the EM itself or asshown in the figure, be fitted on the intake lines for ingredients A andB. In the figure they are labeled VA—viscosity adjusters.

FIG. 18 Writing an Entropic Word The figure show a stretch of mixture oftwo ingredients A and B comprised of 6 letters separated by a dividermaterial. The six letters combine to be a single word.

FIG. 19 Live Entropic Traffic Report The figure shows a truck fittedwith a large screen on which the truck paints entropic message, which ispicked up by over hovering chopper.

FIG. 20 Entropia CCTV This figure shows a large crowd being monitored by9 CCTV cameras which feed into 9 screens. The screen are undergoingcontinuous entropic reading in order to spot unusual occurrence in theCCTV view range. The figure shows a fire erupting in one area of thecrowd. The CCTV camera trained on that area projects the fire on itsscreen (see the red spots). The fire creates a very different entropicreading of the screen, and generates an alarm likely being fed to ahuman monitor. This is a better exploitation of scarce human attention.Instead of getting bored looking at nine repeating screen, the humanexaminer is directed to pay attention to the one camera where theentropic reading showed a big change.

FIG. 21 Entropic Air-Traffic Control This figure shows an air trafficcontrol tower with a projecting cup on which entropic guiding message isbeing displayed and is being read by approaching guided airplanes.

FIG. 22 Significance Orientation Entropic Message This figure shows anentropic canvass with three levels of messages divided by the areadedicated to each message. The most important message A is depicted onthe largest area in order to minimize the chances for mis-reading it.The less important messages, class B are written on smaller area, andthe C class, the least important, are written on the smallest area.

FIG. 23 Uniformity Adjusting in Screen Writing This figure shows amessage area M comprised of 7×9=63 pixels. M shows two ingredients A andB depicted as black color for A and white color for B. Six examples areshown. In all of them the ratio R_(m)=|A|/|B|=21/42=0.5. In the firstexample the uniformity is minimal as all the 21 A pixels are put in onesingle block. In the second case A is divided to two block, higheruniformity . . . and so on until example 6 where the uniformity ismaximized.

FIG. 24: Entropic Mixture of Smooth-Rough Surfaces The top of the figureshows a surface comprised of smooth and rough areas, marked as A and B.The middle part of the drawing shows the difference between the responseof a smooth area of the surface and a rough area thereto. When light(laser or otherwise) is shined on a smooth surface, the light beam isreflected symmetrically, but when the same beam is directed at a rougharea, then the light is scattered. The bottom part of the figure showsan entropic reader comprised of a radiating element that sends a lightbeam to the inspected surface at a prescribed angle, and comprised of alight detector positioned so that it would read the light beam reflectedsymmetrically from a smooth area of the surface. If light is detectedabove a certain threshold then the shined spot is determined to besmooth. Otherwise it is regarded as rough. The contraption glides overthe surface to take a good measurement of the entropic mixture.Alternatively the surface can be made to roll past the detectorapparatus. The apparatus is engineered to cover sufficiently large areaof the inspected surface.

FIG. 25 A Four Smooth-Rough Ingredients Entropic Mixture

This figure shows a surface comprised of smooth area and three grades ofroughness.

FIG. 26 Photoelectric Entropic Reading The figure shows anelectromagnetic radiation E projected onto an inspected surface. Thesurface is comprised of two material ingredients A and B. A is materialwith electrons bonded to their nucleolus so tight that the incomingradiation does not release them. Material B, on the other hand, is amaterial where the electrons are sufficiently loosely bonded to theirnucleus, such that when the radiation E ‘attackes’ them, some electronsget loose. As they become ‘free’ they are pulled up by a positiveelectrode (shown). The resultant current is measured and confirms theidentity of the surface material. The whole contraption glides acrossthe inspected surface in order to perform an accurate reading of itsentropic mixture.

FIG. 27 Asymptotic Reading of Entropic Letters This graph shows theapplication of the differential method for entropic reading. Theentropic reader reads slices in the mixture, M, and applies theprocedure to compute the entropic message—the entropic letter—on M. Whennew slices are added to the measured slices list the computed valuechanges. The figure shows how the value of the letter L oscillate andchanges when a new slice is added to a short list of measured slices,but eventually when the number of slices grows and grows, the value ofcomputed letter L is converging to the asymptotic read of the entropicletter L associated with surface M.

FIG. 28 Superimposing Shape and Shapeless Alphabet The figure showsfirst a shape-based message, the letter “E” expressed in pixels on ascreen. This is done by using a light background as the “page” and adark coloring to draw the letter, “E”, the “ink”. Second it depicts ashapeless message expressed on the same size screen, expressed throughdark and light colors. The idea of the superimposition is that the lightbackground in the shape-based screen is marked with two shades of lightcolor: L₁, and L₂. The human eye intended to read the shape basedmessage will not distinguish between these two shades, but a sensitivecamera will. Also the dark color in the shape-based message will bedepicted with two shades of dark: D₁, and D₂. Again, the human eye doesnot distinguish between the shades but a camera does. In thesuperimposed part of the figure every light pixel in the shape-basedscreen will be written as L₁ shade, except for background pixels thatare marked ‘dark’ in the shapeless screen. These particular pixels willbe marked L₂. In the figure L₂ pixels are represented as “#”. Also, inthe superimposed screen, the “ink” will be marked as dark shade D₁,except for pixels that correspond to the dark shade on the shapelessscreen. The latter will be marked with shade D₂. On the figure the D₂pixels are marked with ‘@’. This arrangement allows a human reader (or acorresponding camera) to read the letter “E” on the screen. All thewhile, the same, or different camera will distinguish between L₁ and L₂shades, and between D₁ and D₂ shades. The latter camera will then countall the pixels that are marked either L₁ or D₁ as one shapeless color,and all the pixels that are marked L₂ and D₂, as the opposite shapelesscolor. All in all the superimposed screen will convey both a shape-basedmessage and a shapeless message.

INTRODUCTION

Shapeless (also called Entropia) is an entropic language based onentropic readings as opposed to shapes and forms. It is robust,versatile, and forge-resistant. The Shapeless language is written intosolid material comprised of at least two distinguishable ingredients.The “pen” for writing the Shapeless alphabet is a device that will mixthe ingredients in constant entropic state throughout the solid lumpwhere the Shapeless message is written. The reader of the Shapelessmessage is a device that can discern the entropic state of the examinedlump where the Shapeless message is written.

The Shapeless message may be used as a means of communication, or morelikely, as a means of material identification—a means to mark a lump ofmatter, to ‘brand’ it, to ‘sign’ it. And as such Shapeless may serve asa useful identification means, preventing errors and forgery. As globalshipping increases in volume, such means of establishing identities ofshipped and transported items increases in importance.

Shapeless is also efficient for analyzing a video stream and spottingsome changes of interest.

Shapeless is a technology, based on the Shapeless language: the means towrite in this language and the means to read in this language, followedby means to make good use of such readings.

Theoretical Foundation

Shapeless can be embodied as a permanent inscription on a solidfoundation, or it may be screen-displayed for quick messaging andcommunication. The method of writing is different, the methods ofreading is similar.

Physical ‘Shapeless’ is based on a mixing apparatus that can delivermixtures of solid ingredients over a range of entropic states. Theseentropic states may be easily read by a proper entropic reader, andverify the identity of the mixed compound by comparing the reading to apre-recorded database.

The technology is based on

1. an effective entropic mixing apparatus 2. difficulty to construct acompound to meet a given entropic state 3. speed, versatility, andreliability of the reader of the entropic states.

Entropic States

Let A and B be two homogeneous distinguishable materials. Homogeneousimplies that both A and B can be identified as material A and B, for anymolecular size and up. Distinguishable implies that upon properexamination there is no confusion whether a lump of matter is A, is B oris neither.

Let A and B also be non-compressible, non-reacting materials. Hence whena volume V_(a) of material A is mixed together with volume V_(b) ofmaterial B, the mixture M, has a volume V_(m) which is the sum of thevolumes of its ingredients:V _(m) =V _(a) +V _(b)

We define a ratio R as:R _(ab) =V _(a) /V _(b)

Let's assume that the mixture M is stable over time. That means it isnot a fluid, but a solid with sufficiently minimal rheologicalproperties.

Every mixture M of materials A and B, has a characteristic ratio,R_(m)=R_(ab)

Let S be a slice, a section, a part of the mixture M (S∈M). Any suchslice S will have a specific ratio R indicating the proportion ofmaterial A, V_(a) (S), versus the proportion of material B, V_(b)(S):R_(s)=V_(a)(S)/V_(b)(S)

The range for R_(s) is: 0≤R_(s)≤∞

For S approaching the full M: |S|→|M|, we have R_(s)→R_(m); Forsufficiently small S, |S|→0, we have R_(s)→0 or R_(s)→∞.

Let S₁, S₂, . . . S_(n) be n random slices of a mixture M where eachslice is of the same volume V_(s)=V_(s1), =V_(s2), . . . =V_(sn).

The respective ratios of these slices is R₁, R₂, . . . R_(n)

Together these ratios are regarded as the ‘ratio set’, ρ=ρ_(n).

The ratio set may be associated with two properties: (i) representativesingle value, R_(m) and (ii) representative uniformity, U_(m). Forexample, the ratio set may be reduced to an arithmetic mean to serve asR_(ρ) and to standard distribution to serve as a uniformity index,U_(ρ).

Given a sufficiently large n (number of slices) the values of theresultant set, ρ, will represent the values of the mixture M that givesrise to the set ρ: mixture ration R_(m), and mixture uniformity U_(m).We designate R*_(m) and U*_(m) as the ratio and uniformity values forthe set ρ that represent the M values. We will address the variousoptions for R*_(m)(V_(s))=f(ρ_(n), V_(s)), and U*_(m)(V_(s))=f′(ρ_(n),V_(s)). The functions f and f′ will allow for asymptotic existence:R _(m)(V _(s))=Lim R* _(m)(n) . . . for n→∞U _(m)(V _(s))=Lim U* _(m)(n) . . . for n→∞

Both values R_(m)(V_(s)) and U_(m)(V_(s)) are characteristics of themixture M.

We regard the pair R and U (ratio and uniformity) of a mixture M ofingredients A and B to together define the entropic state E=F(R, U), forsome well defined function F. E—the entropic value of a bilateralmixture M {A:B} may be regarded as a message carried intrinsicallywithin the mixture. The message can be written by setting up ingredientsA and B in the desired ratio and in the desired uniformity, so thattogether they express the value E. Anyone examining the mixture M willbe able to measure both the ratio R and the uniformity U of M, and,aware of F, will be able to compute E=F(R·U) and thereby read themessage written into M.

Since all these measurements are conducted with a final resolution,there are a finite number of distinct messages associated with such amixture M. We may regard the set of all possible Shapeless messages asthe Entropic Alphabet, or the Shapeless Alphabet. Each distinct messagewill be regarded as a letter of the Shapeless alphabet: L₁, L₂, . . . .

Mixtures can be concatenated, allowing for letters to be grouped intowords, phrases, etc. Such a concatenated construct will be called “AnEntropic Page” or “page”.

M is therefore analogous to the page where a message is normallywritten. Message on a page is normally based on shape-specific lettersand alphabet. The page needs to be well oriented towards its reader,(e.g. to confuse 6 v. 9), and if part of it is torn, part of the messageis lost (e.g. E with the bottom smeared looks as F). Shape-specificletters are vulnerable to erasure and smear of some shape marking,creating confusion or mis-reading. By contrast, the entropic mixture Mmay be bent, cracked, broken, squeezed and otherwise rough handled—itsmessage in written intrinsically and is properly deciphered regardlessof M orientation towards the reader, and also in situations where someof the mixture is hidden or was chipped away. M cannot be inflated,expanded, or retraced because such changes will modify its entropicstate. All in all it is the robustness advantage which attracts interestto this ‘Shapeless concept’ and its associated technology.

Another point of interest is the difficulty of writing a desiredentropic message. Unlike shape based alphabet, this, so named entropicalphabet is not easy to write. Relatively complex technology is neededto set up a consistent mixture M where any part thereto of somethreshold size and up, exhibits the same ratio, R, and the sameuniformity U to express the desired entropic letter (message) E. Inpractice the error level for R and U will have to be sufficiently smallso that the reader will read in M the right message E.

When it comes to protection and against fraud and abuse, the barrier toeasy writing of an entropic message becomes important.

While writing an entropic message is not easy, to read a message is mucheasier, and with proper reading equipment can be done extremely fast andvery efficiently. A measuring device may be exposed to any part ofsufficient size of M, identify a slice of M, and measure R and U. Sinceboth R and U are intrinsic they remain consistent enough (if properlywritten) through every set of examined M parts. Therefore the readerwill be able to focus on a surface portion of M, viewing that portion asa volume of small thickness. All that is needed is for ingredients A andB to represent themselves in a way that projects to a reading devicesuch that both their relative ratio and their uniformity is computablefrom these projections. So A and B may reflect light in differentcolors, or project any other frequency of electromagnetic radiation, orproject particles, like electrons, as long as A and B aredistinguishable from one another and from other material O which is notA and not B.

Let us divide the R_(m) range to I_(r) intervals, and similarly dividethe U_(m) range to I_(u) intervals. Accordingly, a mixture M ofingredients A and B may have I_(ru)=I_(r)*I_(u) distinct identities, asmeasured over n slices cut from the mixture M. In practice I_(u) maydepend on the value of R, the closer R is to unity, the moredistinguishable uniformity values may be observed.

The entropic message E of a mixture M, by default will be regarded asletter L of the entropic or say the shapeless alphabet. Letters can becombined to words, and words to phrases etc. In general E will be theentropic message associated with M.

One may map the Ir intervals chosen for ratio, to be listed each withthe number of associated uniformity measurements Iu associated with thegiven R ratio.

R U

1 X X

2 X X X

3 X X X X

-   -   . . . .

Indicating that for higher R there are more uniformity intervals. Thislist together defines the size the entropic alphabet—the number ofdistinct signals to be written on M.

As a matter of procedure one will need to agree on a response in thecase where a uniformity measurement, U fall too close to the borderbetween two intervals. If U is determined by inspecting a growing numberof n slices, then on will simply inspect more slices. A possibility ofbeing unable to decide on a particular uniformity interval may beaccounted for.

We now define π_(s) as the average ratio of the ratio set:π_(s)=(1/n)*ΣR _(i) . . . for i=1,2, . . . n

Let U be a uniformity index associated with the mixture m. U indicatesto what degree the ratio set is uniform. There are various ways tomeasure uniformity, any one such method can be selected and used to mapinto a range of U values such that U=1 implies perfect uniformity(R₁=R₂= . . . R_(n)) and U=0 implies maximum non-uniformity, namely theratio set contains a member i where R_(i)=0, or contains a member jwhere R_(j)=∞.

Below we will present various ways to define and compute uniformity of amixture. Right now we will define “Persistent Uniformity” as auniformity U(s) computed on the basis of s slices, which converges to alimit U*=U(s→∞).

We also define a “consistent mixture” (M*) as a mixture that satisfiesthe following condition:

Let C be a cut of M such that C>>S. Let C₁, C₂, . . . C_(c) be c cuts ofM. We will regard mixture M as consistent if:U*(C _(i))=U*(M)

for i=1, 2, . . . c

A mixture is regarded as ‘consistent’ if every part thereof shows thesame uniformity.

Let σ be the scale of uniformity values. That means uniformity is sodefined that it can assume one out of σ possible values. In that casethe uniformity of a mixture may be regarded as signal, information. Anelimination of the 1 to σ uncertainty and replacing it with one value. Aconsistent mixture will project the same signal regardless which part ofit was examined.

Ratio and Uniformity Options

The functions f, and f′ mentioned above map the ratio set ρ to mixturerepresentative ratio, R_(m) and a mixture uniformity index U_(m).

We discuss several options for such representation.

1. average and standard deviation.

2. universal ratio, and infinity range

3. differential method

The entropic letter L written by an entropic mixture M is determined bythe ratio between the ingredients A and B and the degree of their mutualdistribution. The ratio, R, is normally simple division of therespective quantities. But a variety of definitions may also be used.For example: R=(Q_(a)+δ)/(Q_(b)+δ), where δ is an agreed constant,designed to prevent division by zero. Or R=(Q_(a))²/(Q_(b))², whereQ_(a), Q_(b) are the quantities of A and B respectively.

There are many ways to determine uniformity. They require marking sliceson the mixture. Such slices may be marked by some order, like tiles, ormay be determined randomly.

Average and Standard Deviation

We can defineR(ρ_(n))=(1/n)*ΣR _(i) . . . for i=1,2, . . . n

And define uniformity as:U(ρ_(n))=1−σ

were σ is the standard deviation of the ratio set, ρ_(n)

Inverse Ratio Method

Given a ratio set ρ_(n): R₁, R₂, . . . R_(n) where R_(i)=V_(ai)/V_(bi).V_(ai), V_(bi) are the volumes of A and B respectively in slice i.

We will normalize the volumes by dividing the volumes by the volume ofthe slice, Vs=|S|:A _(i) =V _(ai)/(V _(s) *R)B _(i) =V _(bi) /V _(s)

V_(s) is the volume of each of the n slices. We shall define theuniversal ration R′ as follows:R(ρ_(n))=(ΣA _(i) /ΣB _(i)) . . . for i=1,2, . . . n

Lemma:R _(m)=Lim(R(ρ_(n))) . . . for n→∞

Proof: Because the n slices are randomly assigned then each element j ofM will be counted by t_(j) slices. And the random slicing dictatest₁=t₂= . . . t_(n)=t so:R _(m)=Lim(R(ρ_(n)))=(t*ΣA _(i) /t*ΣB _(i))=(ΣA _(i) /ΣB _(i)) . . . fori=1,2, . . . n

One may note that the above relationship is universal regardless of thesize of slices, V_(s).

Uniformity may be computed as follows:U(ρ_(n))=1−(⅔)Σ|(A _(i)+1/B _(i)+1)−(B _(i)+1/A _(i)+1)|

As can be seen for 0≤A_(i), B_(i)≤1, we have 0≤U≤1

The higher the value of U the closer A_(i) and B_(i) are to 0.5.

There are computational advantages to this formula as opposed tostandard deviation.

We can write:Lim[U(S)]=1 for S→M, or say |S|→|M|. and also:Lim[U(S)]=0 for S→0, or say |S|→0

The Differential Method

This method is based on the idea that in a well mixed (high entropy,high uniformity) lump, comprised of equal amounts of ingredients A and B(V_(am)=V_(bm)), for any slice, S, not too small, the differenceΔ_(ab)(S)=|V_(a)(S)−V_(b)(S)|→0.

And for the general case where R=R_(m)=V_(am)/V_(bm), for any slice S,not too small the difference: Δ_(ab)(S)=|V_(a)(S)−RV_(b)(S)|→0. ChoosingA and B so that R≥1. V_(a)(S) and V_(b)(S) are the volumes ofingredients A and B in slice S, respectively.

Given a mixture M, one would randomly ‘cut’ n slices S₁, S₂, . . . S_(n)of equal size V_(s)=|S|. Each slice is ‘returned’ to mixture M beforethe next slice is cut. Each slice will be evaluated as to its volume ofingredient A versus the volume of ingredient B: {V_(a): V_(b)}. Therebythe M evaluator will collect 2n pieces of data, the volumes of A and Bin the n slices: V_(a1), V_(a2), . . . V_(an), V_(b1), V_(b2), . . .V_(bn)

Once the data has been collected the M reader will compute its estimateof the ratio value R_(m) of mixture M:R _(n) =ΣV _(ai) /ΣV _(bi) . . . for i=1,2, . . . n

R_(n) will be the reading (the estimate) of the ratio R_(m) of M, perthe information from the n slices.

The Uniformity of M, U_(m), will be computed (estimated) per the nslices through the computed uniformity value U_(n). EstimatingU_(m)=U_(n). U_(n) is computed as follows:U _(n)(S)=1−(1/(n*V _(s) *R _(n)))Σ|R _(n) V _(ai) −V _(bi)| . . . fori=1,2, . . . nAnalysis: the greatest uniformity happens when the A and B ingredientsare of same amount, namely the ratio is unit (R_(n)=1), and within everyslice within the n evaluated slices, the quantity of A will be equal tothe quantity of B: V_(ai)=V_(bi) for i=1, 2, . . . n In that case allthe added members: |V_(ai)−V_(bi)|=0, and the uniformity U=1.Uniformity will be zero, when the ingredients A and B are of equalamount, R_(n)=1, and when every examined slice among the n slices willbe full of either ingredient A or ingredient B, but not both. In thatcase we have: |V_(ai)−V_(bi)|=V_(s)In that case we have:U _(n)(S)=1−(1/(n*V _(s) *R _(n)))Σ|V _(s)| . . . for i=1,2, . . . nU _(n)(S)=1−(1/(n*V _(s)*1))(nV _(s))=0

All the other cases are in between 0≤U≤1

Illustration

We reference FIG. 1 where a mixture M of size 4×4 squares is comprisedof ingredients and A and B at a ratio of 1:3. In FIG. 1a the mixture isnot very uniform. A appears in M in chunk of 4 contingent squares. InFIG. 1b , the mixture is more uniform, A appears as individual squares.

The two cases are analyzed by cutting from M n=10 slices of size 4squares each (V_(s)=4). Each slice is analyzed per volumes A and B init. The readings for FIG. 1a are: 0-4, 1-3, 0-4, 2-2, 2-2, 2-2, 0-4,0-4, 0-2, 0-4

Accordingly we have R_(n)=26/7=3.71, which serve to estimate theaccurate ratio R_(m)=3 (in practice one will have much larger n valuesfor much better accuracy). Entering into the uniformity formula:

Cutting the same 10 slices over the distribution in FIG. 1b , wherethere is greater uniformity we acquire the following readings: 1-3, 1-3,2-4, 0-4, 3-1, 1-3, 0-4, 0-4, 1-3, 1-3

Accordingly we have R_(n)=32/10=3.2, which is a better estimate forR_(m) (=3.0), as expected because of the increased uniformity in thiscase. We then compute:U _(n=10)(S)=1−(1/(4*3.2*10))*24.0=0.82

As expected the uniformity of this one square size distribution ishigher than the 4 contingent squares distribution shown above.

The same mixtures were then analyzed with 10 slices of a large sizeV_(s)=6. The results as shown in FIG. 1c are: 1-5, 2-4, 2-4, 4-2, 0-6,2-4, 4-2, 0-6, 1-5, 1-5.

Accordingly we compute R_(n)=43/17=2.52, a rough estimate for R_(m)=3.The uniformity is computed as follows:U _(n=10)(S)=1−(1/(6*2.52*10))*38.72=0.75

Similar to the uniformity achieved for the smaller slice (V_(s)=4).

The same slice size |S|=6 is used over the more uniform mixture as inFIG. 1d . The result: 1-5, 2-4, 1-5, 1-5, 2-4, 2-4, 2-4, 1-5, 2-4, 4-2.

Calculating R_(n)=42/18=2.33 The uniformity is computed as follows:U _(n=10)(S)=1−(1/(6*2.33*10))*19.26=0.87

Checking the same with a larger slice |S|=8. As in FIG. 1 e: 0-8, 1-7,1-7, 4-4, 2-6, 2-6, 4-4, 4-4, 0-8, 4-4.

Calculating R_(n)=58/22=2.63. The uniformity is computed as follows:U _(n=10)(S)=1−(1/(8*2.63*10))*26.20=0.87

Checking the same with a larger slice |S|=8 over the more uniformdistribution as in FIG. 1 f: 1-7, 2-6, 2-6, 2-6, 2-6, 1-7, 2-6, 2-6,1-7, 2-6

Calculating R_(n)=63/17=3.70. The uniformity is computed as follows:U _(n=10)(S)=1−(1/(8*3.70*10))*19.70=0.93

This illustration shows that for all sizes of slicing the uniformityratings are higher for the case of separate squares relative to the caseof blocks of 4 squares together.

The Size of the Slice

The entropic reading of a slice S of the entropic mixture M is stronglydependent on the size of S. Clearly:|S|→0:R _(s)→{0,∞},U _(s)→0

where |S| is the volume size of S, R_(s) is the recorded ratio betweenthe entropic ingredients A and B, volume-wise in S, and U_(s) is theevaluated uniformity between A and B within S. This is because the sizeof the slice becomes so small that it becomes 100% constructed fromeither A or B.

Equally clearly is: |S|→|M|: R_(s)→R_(m), U_(s)→U_(m)

Obviously when the slice approaches the dimensions of the mixture, itsattributes approach the attributes of the mixture.

The measuring methodology presented here is based on random examinationsof some n slices, where n→∞ for maximum accuracy. In practice, when theresult is stable when more and more slices are added then n appearslarge enough. We use these n measurements to first estimate R_(m), theratio for the examined mixture. R_(m) is best estimated by adding allthe A volumes in the various slices and dividing it by all the Bvolumes. For this method to work it is not important to keep the size ofthe slices the same.

To estimate the uniformity of M it is necessary to compare R values forthe n slices, and here it is important to keep the slice size fixed. Thegreater the spread of these n ratio values the lower the uniformity.

Generally the aim is to extract as many distinct entropic measurementsfrom a mixture. Therefore one seeks the slice size that would result inas many distinct measurements as possible. This optimum slice size isclearly not at the bounds. A very small size will show low uniformityregardless of the uniformity of the mixture, and a size close in size tothe mixture will show high uniformity, regardless of the uniformity ofthe mixture. So an in between optimum is sought. This optimum may dependon the size of the smallest measured volume, but also on R_(m). Theoptimum size size S_(o) may be found analytically or experimentally.

Consequently: for 0≤|S|≤|M|, 0≤R_(s)≤R

The Iterative Entropic Protocol

The entropic message, E, or say the letter L of an entropic mixture M isdetermined through two variables: the ratio between the two ingredientsA and B, and the distribution of A and B. n slices are marked on M: S₁,S₂, . . . S_(n).

Procedure: for n=1, mark S_(n), compute the ratio R_(n) for that slice.Since it is one slice the uniformity is U_(n)=1.

Increment n to n=n+1, now n=2, mark slice S_(n) on M (randomly or byorder), compute the ratio R_(n) by adding the quantities of A throughthe slices, and the same for the quantities of B, and divide the twonumbers.

Based on the uniformity method chosen use R_(n) and the values of thequantities of A and B in all the marked slices to determined theuniformity based on the marked n slices: U_(n).

Compute the entropic letter written on M, L, from R_(n) and U_(n):L_(n)=f(R_(n), U_(n)).

Increment n again: n=n+1, mark another slice on M and repeat as beforeto compute R_(n) and U_(n), for the incremented value of n.

The repetition above yields a series of entropic letters. Let theentropic alphabet be comprised of t letters:L ₁ ,L ₂ , . . . L _(t)

And the series of letters computed over M as above is:L′ ₁ ,L′ ₂ , . . . L′ _(n)

If n is incremented so that:L′ _(n) =L′ _(n-1) = . . . L′ _(n-d)

For some agreed upon d=4, 5, . . . then L′_(n) is the letter associatedwith M.

The procedure: Keep incrementing n until the above condition is met. Ifn is incremented more and more and no convergence is observed (by apreset limit), then the computing machine outputs a ‘failure’ signal.

Multiple Ingredients Entropic States

So far we discussed the binary case: ingredients A and B are mixed intomixture M. We concluded that such a mixture could be marked by an“entropic alphabet” containing I_(ru) letters, or say be marked by oneof I_(ru) distinct numbers.

We shall now expand this situation to c components where c>2: C₁, C₂, .. . C_(c) mixed together into a mixture M. Every pair of ingredients canbe used to indicate I_(ru) letters, or say messages, or signatures.

This amounts to an entropic language comprising L messages:L=(0.5*c!/(c−2)!)*I _(ru)

Which will allow for 4500 messages to be marked on a mixture of 10ingredients where I_(ru)=100. (Or say an entropic alphabet of size4500).

Note: we use the term ‘component’ or ‘ingredient’ in this entropiccontext interchangeably.

Ratios Only Language

The main idea in this Entropia (Shapeless) concept is the combinedletter based on ratio reading between bilateral ingredients and thedegree of uniformity of their distribution in the mix. The ratioinformation survives when the mixture is deformed, or re-mixed. Theuniformity information does not. This raises the option to rely on ZeroEntropic language—ignoring the entropy, and reading only the ratios.

The language size |L| in that case will be I_(r) for the bilateral case.In the case where c components are mixed the number of distinct messages|L_(c)| will be:|L _(c) |=I _(r) ^(c-1)

Combination Enhancement

Any group p of the c ingredients that are mixed into M may be viewed asa single ingredient A, with any number q of the remaining c-pingredients being viewed as an opposite ingredient B. In other words,one can treat any p ingredients as a single bilateral ingredient andsome other q ingredients to be treated as the opposite bilateralingredient B.

We can write: 1≤p≤c−1, and 1≤q≤c−p.

Such properly defined combinations of ingredients will allow for moreI_(ru) signals to be projected from the mixture.

There are c!/(p!*(c−p)!) different sets of p elements out of c for agiven value of p. For each such selection the q ingredients are selectedfrom the remaining c-p ingredients, there are 2^(c-p) such combinationsand hence, using combinations, a mixture of c ingredients could bemarked with |L| entropic letters:|L|=0.5*I _(ru)*Σ(c!/((c−p)!p!)*2^(c-p) . . . for p=2 to p=c−1

The multiplication by 0.5 is to account for the fact that everyingredient is counted twice, once as being in the p group and once beingin the q group.

Top-Down Entropic Selection

Let one mix n=2^(t) components c₁, c₂, . . . c₂ ^(t). One will thendivide the n components to two groups G0 and G1, where G0 includescomponents 1 to n/2, and G1 includes all the rest. Counting each memberof group G0 as ingredient A and each member of group G1 as ingredient Bin an entropic setting, one would then have complete freedom to assignan entropic message E to be written over the two ingredients A and B.Namely one could use any desired ratio, and mix the two ingredients inany desired uniformity.

Next one could divide group G0 to two groups G00, and G01, where G00contains ingredients 1 to 2⁴, and group G01 contains all the rest. Onecould regard all the members of group G00 as representing ingredient A′,and all members of group G01 as representing ingredient B′ in anentropic setting, and have the complete freedom to use any ratio R′ andany uniformity index U′ to express any entropic message E′ between thesetwo groups, G00 and G01.

Similar division to two groups of equal size can be done over group G00,and then on and on, dividing any group to two sub-groups taking theroles of the entropic ingredients A and B, and continue with thisdivision until there are only two ingredients in a group. Each of theseactions will allow an entropic writer to use any desired message, orsignal for each such binary entropic setting. This amounts to having2^(n-1)−1 entropic messages of any desired value written into a mixturecomprised of n ingredient.

This is strictly true for n being an exponent of 2. But any other valueof n will do, since it is not required to divide ingredients to equalsize groups. So n=16 is divided to two groups 8 ingredients each. Andeach such ground is divided to two sub groups with 4 ingredients ineach, which is further divided to 2 groups containing 2 ingredientseach: 8-8, 4-4, 4-4, 2-2, 2-2, 2-2, 2-2

But for n=17 one could divide to a group of 10 v. a group of 7 anddivide the 10 to 5 v. 5, then to 2 v. 3, while dividing the 7 to 3 v. 4and dividing the 4 to 2. v. 2: 10-7, 5-5, 2-3, 3-4, 2-2

It is noteworthy that while the above described counting only counts“degrees of freedom,” namely bilateral entropic relationships that canbe determined irrespective of any other entropic messages, in generalthere are, many more readings based on any subgroup of ingredientsversus any other subgroup of such ingredients.

Tracing

Let a mixture M be comprised of three ingredients: A, B and O. M can beentropically analyzed per ingredients A and B, disregarding the “other”,O. Any slice S of M will have some measure of volume for A and somemeasure of volume for B, and these volumes will define a ratio R_(ab)between these two ingredients. A set of some n such slices will showsome measure of uniformity of these R values, so that one could examineM and read in it an entropic message E based on the distributions ofingredients A and B within M.

The above is true even if A and B are small volumes compared to O. Thatmeans that one could mark a material O with an entropic message E byinjecting into O trace amounts of two ingredients A and B.

Dimensional Reduction

Let an entropic mixture M express an entropic letter L. Let W be anarbitrary slice of M (W∈M). If the entropic letter of such W is also L,then we says that W is a proper entropic subset of M. Obviously if W′ isa proper entropic subsets of M and W″∈M is larger than W′(|W″|≥|W′|)then W″ is also a proper entropic subset of M. Every M is associatedwith the smallest proper subset below which the entropic message isdifferent, W_(min).

Given a mixture M comprised of a three-dimensional body, every properentropic subset thereto, W, will be evaluated to project the sameentropic letter L. This implies that an entropic reader exposed only toa W_(min) size of M or higher will be able to read the letter carried byM.

Since all the analysis above was carried out without any restriction onthe shape of the proper entropic subset, one can choose a subset of nearzero depth and any size of the other two dimensions. In other words onecould use a ‘skin’ type W, a surface. This has practical implications,allowing an entropic reader to read the surface data of a mixturewithout bothering to look inside. It also implies that cutting M to twosuch that the newly exposed surface is larger than W_(min) will allowthe entropic reader to read E on the exposed surfaces.

Same as the reduction from a three dimensional mixture to a twodimensional subset, so a two dimensional subset may be reduced to a bodywith two small dimensions and one long dimension, like a rope, as longas the volume in total is equal or larger than W_(min).

Material Verification Setting

We consider a physical solid element X that is known to be in alocation, L and time t. As it turns out element X may be located inlocation L′ at time t′:X(L,t)→X(L′,t′)

Owing to the gap in location (ΔL) and/or in time (Δt), there exists apossibility that what is represented as X, is in fact a differentphysical element, X′≠X.

In other words, over time and over distance element X has been replacedwith element X′. Intentionally or by mistake.

In order to make this scenario unlikely one would look for a property Pof X (P_(x)), such that the corresponding property for X′ (P_(x)′) willbe different: P_(x)≠P_(x)′

If such a property P is found then in the case where P_(x)=P_(x)′, thelikelihood that X≠X′ is minimized, and in the case where P_(x)≠P_(x)′the likelihood that X≠X′ is very high.

We conclude then that examination of such property P of some entity Xover some distance ΔL and over a time interval Δt, is an effective meansto verify identity of physical entities over shipping distances and overtime.

Clearly, if more properties of X are found, P′, P″, . . . and eachindependently verifies the identity of X, then the confidence in thisdetermination grows.

We will discuss below various mechanisms for a switch X→X′, and presentthe entropic state as an effective property P to verify some entity X.

Material Switch Options

An entity X may be switched to another entity X′ over space and time,via:

1. innocent replacement 2. mistaken replacement 3. intended replacement.

The most worrisome option is ‘intended replacement’ because the replacermay be smart and resourceful, replacing the original entity X with areplacement X′ that will very likely be regarded as the original entityby the down the line examiner.

To frustrate such an intending replacer it is necessary to do one ormore of the following protective steps:

1. Deny access

2. Conceal the identity of the verification property P

3. Make it too costly to construct a replacement entity X′ that wouldpass as X.

We claim that Shapeless—the solid signature technology is an effectivemeans to verify identity and detect replacement.

The Entropic State Property

We have presented mixture M, of two ingredients A and B which arecharacterized by two factors R_(m)(V_(s)) and U_(m)(V_(s)), where V_(s)is the volume of each of the n slices cut out of M.

We have seen that the mixture M can be characterized by I_(ru) distinctletters. Such letters may be regarded as the entropic signature of themixture M: E(M). That means that a set of t mixtures M where t≤I_(ru)may be uniquely marked through distinct mixtures of components A and B.The chance of an arbitrary person to guess the correct signature of M is1/I_(ru). Accordingly, entropic state technology (Shapeless) may be usedfor material identity verification.

The Shapeless technology does not rely on any shape, size or forumattributes of the identified entity. The solid entropic mixtureverification signature cannot be wiped off, marked away, washed,removed.

Material Verification Protocols

We may divide Shapeless verification protocols per number of partiesinvolved: discerning three types: 1. single party verification protocols2. bilateral verification protocols 3. Multi-party verificationprotocols

We may also divide Shapeless verification protocols to: 1. selfcontained 2. Seals 3. Stamps

We also add ‘complex verification protocols’ 1. Verifying fluids 2.Combined Entropic Mixtures 3. Chemical Cryptography Entropia.

Party Count Classification of Protocols

Discerning:

1. single party verification protocols 2. bilateral verificationprotocols 3. multi-party verification protocols

Single party protocols are usually designed to prevent mistakes andconfusion. As well as uncalled for intervention of a second party. Theymay be invoked on a time interval basis, or they may be invoked perevents. Bilateral verification protocols are designed to safeguardshipping integrity of a shipped package. Multi party verificationprotocols are designed to handle items changing many hands, orsplittable items.

Bilateral Verification Protocols

Of three modes:

1. call-back 2. send-along 3. public ledger

In the first mode the recipient calls the dispatcher who instructs therecipient which entropic measurements to take. The measurements arerelayed to the dispatcher who compares them with its prior measurementsand accordingly notifies the recipient whether the package is authenticor not.

In the second mode the dispatcher sends the entropic measurements with,or in parallel with, the entropic package for the recipient to verifyintegrity.

In the third mode, the dispatcher publishes the entropic measurements sothat anyone who takes custody of the package can verify its integrity.

Multi Party Verification Protocols

Multi party verification protocols are designed to handle items changingmany hands, or splittable items.

Chain of Custody

A package may be sent from a dispatcher D to targets T₁, T₂, . . .T_(g), sequentially in a fixed or unfixed order. Every target(recipient) will be able to verify the identity (integrity) of thepackage. The g targets may share verification data with the dispatcher,and each will verify the package in turn. The verification data, (theentropic signature, Ω(package)) may be the same for all g recipients:Ω(package)₁=Ω(package)₂= . . . Ω(package)_(g)

or it may be different:Ω(package)₁≠Ω(package)₂≠ . . . Ω(package)_(g)

or a combination thereto. Different signatures may be arranged viapackages marked with c components, and each recipient is checking adifferent bilateral entropic pair. This will be important when thedispatcher wishes to authenticate proper receipt of a package by each ofthe g addressees. When an addressee will claim receipt of the package,the dispatcher will ask it to read particular measurement within a rangeof multi-ingredients measurements, and then authenticate the receipt bycomparing the reported measurement to the dispatcher database. If eachtarget is asked a different set of measurements to measure (and report)then two or more targets cannot collude to cheat the dispatcher.

Illustration. A dispatcher D sends an entropic package to six recipient(targets) T₁, T₂, T₃, T₄, T₅, T₆. D prepares the package as a mixture ofthree ingredients C₁, C₂, C₃. When T₁ receive the package, D asks themto take the entropic measurement based on the bilateral entropic readingbetween C₁ and C₂ {C₁:C₂}. T₁ passes the reading to D who measured itbefore the dispatch and now verifies that T₁ receives the package sentto them by D. T₁ then passes the package to T₂. D then asks T₂ tomeasures the entropic reading based on the bilateral entropy between C₂and C₃: {C₂:C₃}. Again D compares the reading to its own measurementbefore the dispatch.

The package then moves from target to target.

For T₃ the communicated measurement is {C₁:C₃}

For T₄ the communicated measurement is {(C₁+C₂}:C₃)

For T₅ the communicated measurement is {(C₁+C₃}:C₂)

For T₆ the communicated measurement is {(C₃+C₂}:C₁)

Splittable Verification

An entropic mixture with a μ level consistency can be split to 1/μparts, where each part is sent to another recipient. Practicing severalcases of bilateral specification.

The entropic signature (Ω) is in general a combination of entropicmessages forming a word.

Functional Classification of Protocols

We may also divide Shapeless verification protocols according tofunctionality:

1. self contained 2. Seals 3. Stamps 4. tracings

Self contained entropic packages are intrinsically marked with theentropic message. For example, medical pills can be colored green andred and the bilateral entropy is measured. Entropic entity may befashioned as seals to verify the integrity of what is beyond the seal.The entropic entity may be a “stamp” attached to a device, mainly forthe purpose of easy tracking.

Tracing

The entropic ingredients A, and B, may be tracers injected into a third‘carrier’ ingredient C. C may be a solid bulk, or it may be a liquid. IfC is a turbulent liquid then reading will be limited to analyzingindividual trace lump for their entropic message. If C is solid, or is alaminar flow liquid, then reading will also extend to the number of A-Btracers per inspected area or volume of C. If C is transparent thenvolume reading is feasible.

Complex Verification Protocols

We also add ‘complex verification protocols’

1. Verifying fluids 2. Combined Entropic Mixtures 3. ChemicalCryptography Entropia

A container with fluid F may be injected with c highly viscous fluids:C₁, C₂, . . . C_(c). The combined material is then frozen into solid,and shipped (frozen). At the receiving end the frozen material isexamined for its entropic messages, to verify identity.

Illustration: a transparent solution of a biochemical identity, H, isinjected with two highly viscous pastes that do not react with H. Thepastes are one red and one green. The injected H is frozen and shipped.The recipient, before unfreezing the container, takes an entropicreading of its red-green signature and compares it to the measurementtaken at the dispatch. If the measurements agree, then the recipient isassures of authenticity. The package is unfrozen, and injected pastesare being removed and B is used as intended.

Combined Entropic Mixtures

To increase security and reliability one could combine entropic mixturesin many ways.

For example one could use a self-contained mode entropic signature tomark a given entity as a mixture M, then put M in a container sealed byan entropic mixture M′, which again might be sealed by a second entropicmixture M″, etc.

Also entropic messaging can be done through regular camera reading orthrough any other electromagnetic radiation. It can be done through thephotoelectric effect where ingredient A is releasing electrons withenergy E_(a) upon being shined with a given electromagnetic wave, whileingredient B is not. A current detector will spot whether the areashined is A or B.

Chemical Cryptography Entropia

Using biochemical mechanism an entropic mixture may be comprised of ccomponents C₁, C₂, . . . C_(c). Each of these components has abiological activator: A₁, A₂, . . . A_(c). The dispatcher and therecipient may have shared the identities of the c components and theiractivators so that they can measure the entropic entity secretly. Otherswill not be able to carry out such measurement.

Entropic States Verification Technology

This technology is based on effective construction of an entropic mixerand an entropic reader.

We regard one party as the ‘preparer’ or ‘shipper’: the party thatprepares an entity X at time t at location L. We regard a second partyas the ‘recipient’ or the ‘verifier’: the party that examines X againsta replacement scenario at time t′ and at location L′.

We envision the preparer preparing X with entropic state U, shipping itto the recipient who is reading the shipped entity for its entropicstate. The shipper and the recipient compare notes and if they bothagree on the entropic state of the entity, they both regard therecipient held entity to be the entity shipped to them by the shipper.If the uniformity states don't agree, a replacement scenario issuspected.

We now discuss the entropic mixing technology and the entropic readingtechnology.

Entropic Mixing Technology

Discerning between:

1. Two dimensional entropic mixtures 2. Three dimensional entropicmixtures.

To prepare an entropic mixture one could opt to one of the followingmethods:

1. Mathematical Modeling 2. Entropic Mixing

One could construct a 2D or 3D model to entropically mix c components,then feed the result to a 2D or a 3D printer as the case may be andproduce the entropic message. Using a specially designed entropicmixture one could create an entropic mixture of desired readings. Thereare other ways to construct an entropic message based on mathematicaldescription.

Mathematical Modeling

One can build a deterministic mixture of c components such that theywill satisfy a series of entropic values. Clearly for an even c onecould define c/2 pairs and solve the mathematical challenge of occupyinga volume V_(m) with the c components such that the entropic values forthe c/2 pairs fit any desired list of E(1,2), E(3,4), . . . E((c−1),c).

We have discussed the case of c=2^(t) t=1, 2, . . . dividing thecomponents to two groups G₁ and G₂, of 2^(t-1) each, one may build amathematical solution for the requirement E(G₁, G₂), and so on untilthere are two ingredients.

There are various ways to use mathematical modeling to build a desiredentropic mixture. We discuss:

-   -   1. Cartesian building blocks 2. polar building blocks 3. random        inflation

Once the mathematical model of M has been built the result is thentranslated to a 3D printer feed to construct it.

Math modeling is essential for computer screen Entropia

Cartesian Building Blocks

In this method one divides a designated volume M to cubes of size δ³,where δ is an arbitrary measure. M is then comprise of m=xyz such cubes,where x=M_(x)/δ, y=M_(y)/δ, and z=M_(z)/δ, where M_(x), M_(y), and M_(z)are the lengths of M in the three spatial directions x, y and z.

Under this representation the maximum uniformity that can be laid out iswhen each adjacent cube is of alternative color (we use the term color,to indicate ingredient because in many practical applications thedistinction of the ingredients is done via their color). Of course ifthe slices, S₁, S₂, . . . are of size V_(s) where V_(s)<<δ³, then, thesmaller V_(s), the less the uniformity reading of the mixture. Howeverfor V_(s)>δ³ the uniformity reading will be the highest U=1.

It is now possible to re-assign the colors of the cubes according tosome chosen formula where a group of adjacent cubes will share a color.The larger those groups, the lower the uniformity reading per a givenslice side. In fact when the grouping is of of t cubes such thatt*δ³≥V_(s), then uniformity is approaching zero.

Given a choice method for measuring and computing the entropic message Eone could model a given color assignment of the m cubes so that theentropic message will be the desired value E.

Note that we use the term message, signal, or letter, interchangeably todenote the information carried by the entropic value E.

The modeling may be stochastic, using random (Monte Carlo) procedures.

The modeling do not necessarily have to be mathematically precalculated. One could choose a block size (value of m adjacent cubes ofsame color), then run a metric measurement of the assigned M values (seeillustration). The value of R is easy. The value of U (uniformity) maybe readily achieved by increasing the value of m if one wishes thedesired value of U to be lower than the model indicates. And converselyone would decrease the value of m in order to achieve a higher value ofU than is currently measured and computed. This is a classic feedbacksequence leading to the desired result.

The designer may also play with the shape of contingent blocks. Theydon't have to be larger cubes, or ‘bricks,’ they may be of any shape.One could also use various size blocks and of different shapes, thenMonte Carlo model the mixture (the same feedback sequence). The ratio isassigned without difficulty. As to the uniformity. If one wishes it tobe larger than what is measured then randomly one would cut down thesize of a few blocks of equal color blocks, and measure again. It can berepeated until uniformity is coming close enough to the desired.

Same for the opposite direction if one wishes for the mixture to haveuniformity U lower than what is measured, then one would patch togetherlarger blocks of same color cubes.

By adjusting the sizes of the blocks one could adjust the value of theuniformity to be what one desires it to be.

In practice the entropic reading may be conducted over 2 dimensionalsurfaces, and in that case the cubes will be replaced with squares ofsize δ², but otherwise the procedure are very much the similar. Furtherreduction may be achieved by collapsing the mixture M into a onedimensional stretch. The basic S elements will then be uni-dimensionalintervals.

Polar Building Blocks

Everything discussed over Cartesian elements of M is applicable overpolar elements of M. The choice of coordinates depends on theapplication. If the mixture M is a rolling ball then it is moreconvenient to mark its surface with polar coordinates.

Random Inflation

In this method one uses ingredient A as ‘carrier’ namely by default M is100% ingredient A. Then one randomly assigns some m ‘points’ (smallelements in M) with color B in order to satisfy the desired ratio, R. mis selected so that the B points are uniformly peppered throughout M.Next one randomly increases the size of the B ‘points’ to largervolumes, or random shapes and eliminates the smaller B volumes tomaintain the desired R. After such increase one runs a Monte Carlo modelto read the entropic message of M. The B points are randomly inflated(while eliminating the smaller volumes), again and again until themeasured uniformity fits the desired uniformity. If an overshoothappens, then one randomly splits the largest blocks of B and measuresagain. This feedback sequence will achieve the desired entropic messageon the mixture M.

Clustering

In this method one divides a target mixture M to m volume elements of asufficiently small size, and then randomly populates them with colorassignment according to the desired ratio: R=m_(a)/m_(b) whwerem=m_(a)+m_(b)+m_(o), which are the number of A elements, B elements, andother elements. This will create the highest uniformity per the size ofthe elements. If lower uniformity is desired then, one will randomlypick c “cluster points” in the mixture M. Each of the m volume elementsidentified in M (shape is based on which coordinate system is beingused), will be identified per its distance from each of the randomlychosen c cluster points. This will define c*m distances. The c clusterpoints will be set in an arbitrary order. Then one will identify theapproximately h=m_(a)/c elements of color A for which their distancefrom cluster point 1 is the minimal. And then one would move theseelements along the distance from cluster one, such that the distancefrom cluster one to each of the elements is shrunk by an arbitrarymeasure σ. Same procedure will be repeated with respect to cluster point#2. One will choose approximately m′_(a)/c elements, where the m_(a)′ isthe number of elements not associated with cluster point 1. Same appliedover the remaining elements of color A with respect to the remainingcluster points. When the procedure terminates, then the elements ofcolor A will be more clustered then the before, around the c clusterpoints. This will result in a lower measured uniformity. By repeatingthis procedure, the uniformity will further decline. This can be doneuntil the c cluster points represent c blocks of color A elements. Ifthe resultant uniformity is not sufficiently low, then these c clusterpoints can be regarded as the original distribution and a new set ofc′<c cluster points is marked on M, and the above procedure is repeated.There are several other clustering methods. They all fit into thefeedback sequence designed to generate the desired uniformity figure.

Entropic Mixing

We describe mixing technology wherein two ingredients can be mixed in adesired mutual ratio, R, and where the uniformity can be measured andadjusted at will. The apparatus, called ‘the entropic mixer apparatus’(EMA) is comprised of an entropic mixer element (EM) into which twoingredients A and B are fed, and which outputs a mixture M of A and B.The ratio in the mixer is determined by the feed ratio betweeningredients A and B.

The EMA includes a mixture control unit the “Entropic MixtureController” (EMC), which controls the feed rate of the ingredients A andB, and controls uniformity parameters (“up”) that dictate the operationof the EM.

The EMA also includes an entropic reader, ER, which reads the outputflow from the EM, and feeds the reading to the EMC. Based on the readingof the ER the EMC adjusts the uniformity parameters, “up”, which in turnresults in a new level of uniformity in the output stream. The new levelis read by the ER, and the readings are fed into the EMC, which thenre-adjusts the “up”, and so on until the EMA reaches the desired levelof uniformity, and of course the desired level of ratio. Together theratio, R and the uniformity U, comprise the entropic message E carriedby the output stream. As long as the ‘up’ is kept at its position, theoutput remains as carrier of the desired entropic message (entropicletter).

The properly mixed output is then carried to the entropic form shaping(“the entropic shaper”, ES).

The ES will mold the mixture to the desired form. It may be a threedimensional body or a two-dimensional pasting.

The stable message may also be called an entropic letter. The sameletter is generated as long as the ‘up’ of the EMA are kept stable.

Ahead we discuss the issue of viscosity, and writing complex messages.

Viscosity

The entropic mixing works in a rather narrow band of viscosities. If theingredients are too viscous, or brittle, entropic mixing cannot beachieved. If the viscosity is too low the desired entropic mixing cannotbe fixed. The ingredients will continue to mix and increase the apparentuniformity.

The desired viscosity though must be secured during the mixing only. Theresultant mixture may be solidified and made permanent. Accordingly andEMA may include a heater that would heat the ingredients in order todecrease their viscosity to be amendable to mixing. The mixture willthen be allowed to cool off and solidify. The mixer may be fitted on theEM or on the feeding line for A and B. If the viscosities are too low,the heater may be replaced by a cooler to bring the viscosity to thedesired range.

Complex Entropic Messaging

We have seen that for any given entropic situation, a mixture can haveI_(ru) possible values. So each value may be regarded as a letter, whilethe set of all possible letters is regarded as the entropic alphabet.One would write a codebook matching any of the I_(ru) letters of theentropic language with a particular meaning as the circumstancessuggest.

We now describe how to write ‘words’—combinations of entropic letters.An entropic word W will be concatenation of some w letters:W=L ₁ ∥L ₂ ∥ . . . ∥L _(w)

The description above relates to an EMA which generates a mixture usedto calibrate the entropic message of the EMA. This calibration mixtureis useless, it is ‘entropic junk’ (ej). Once the output expresses theright message then the message is right. The EMA may mark this point byinjecting a divider feedstock, D that would separate between the junkflow and the proper message flow.

When the EMA wishes to change from letter L₁ to the next letter, L₂, itagain goes through junk output while it adjusts the ‘up’ to write thedesired letter. (If the letter was written before then the adjustment isfast and efficient and the junk between the letters is minimal).

Before outputting the junk, the EMA will again send a shot of dividermaterial D. This will result in letter L₁ enclosed between two shots ofdivider ‘fences’. After the second divider comes new junk while the EMAadjusts the ‘up’. When the output is calibrated to generate the desiredletter L₂, the EMA injects another shot of the divider. Now the junkstuff is enclosed between two dividers, and the new mixture flowing outof the EMA is now adjusted to letter L₂. The transition between letterL₂ and letter L₃ works the same way.

In summary, the entire word W will written on a continuous flow of themixture that looks as follows:W=L ₁∥Junk∥L ₂∥junk . . . junk∥L _(w)

This mixture flow then goes through an entropic “junk remover” (“JR”),resulting in the readable letter W:W=L ₁ ∥L ₂ ∥ . . . ∥L _(w)

Words may be added to statements. A statement S will be written as aconcatenation of some s words:S=W ₁ ∥W ₂ ∥ . . . ∥W _(s).

The separation between one word and the next will be marked either by asecond type of a divider material interjected between the words, or bythe same divider but with some distinct marking, like larger quantity.

Sentences may be linked to paragraphs and so on.

The Uniformity Parameters

We describe the “up” (uniformity parameters) for the presented entropicmixing apparatus.

The main control variables are the rate of pumping in the twoingredients A and B. The ratio of the rates expressed in volume persecond for A and B determines the ratio between A and B in the resultingmixture:R _(ab)=(ΔA/ΔT)/(ΔB/ΔT)

where T expresses time. This is a straight forward way to set up thedesired ratio, R for the mixture. This flow rate is determined bysetting the pressure that moves the ingredients A and B. The flowingingredients will have to be viscosity adjusted so that the outputuniformity of the mixture will be durable.

The next parameter is the size of the aperture in the stationary discfor both A and B. The larger the aperture the more material is pushedthrough when the corresponding rotating screen is creating an opening.How much is coming through depends on the pressure difference across thetwo discs, and on the viscosity of the ingredient. This viscosity can becontrolled through the EMA viscosity adjuster (heater or cooler). Byheating up the apparatus the viscosity of most ingredients will go downand more material will come through the aperture.

The EMA may be of the kind where the aperture is fixed and so one needsto change the stationary disc or the rotating disc to change the flowopening. But in the case where the aperture is dynamically controlled(like a camera shutter) then the electronic controller will be able toset the aperture size dynamically. Shutter type discs will have to beengineered hard enough to withstand the pressure difference across thedisc.

Next control parameter is the rotating speed of the rotating disc thatis fitted on the same axis as the stationary disc and is closelyadjacent to it. The faster it rotates, the smaller the amounts of both Aand B that proceed to the first mixing chamber. Hence the smaller theblock of unified material that goes into the mixing. This means that theuniformity of the mixture will be greater. We note that material goesthrough only when the opening on the rotating disc overlaps the hole ofthe stationary disc. The stationary disk has at least one hole foringredient A and one hole for ingredient B. As the rotating disc's holeoverlaps with the A-hole, A ‘paste’ is flowing through the post discmixing chamber as determined by the size of the flow opening and thepressure gradient across the discs. And then the rotating disc rotatessuch that its opening overlaps the hole in the stationary disc where theB ingredient is flowing though, and a bulk of ingredient B flows throughuntil, like what happened with A, the rotating disc rotates further, andits opening does not overlap the stationary disc hole. Then the rotatingdisc rotates again and another chunk of first A and then B is flowing tothe next chamber of the entropic mixer. The rotating disc is adjacentand abreast the stationary disc.

The next control parameter is the relative speeds of the two rotatingdiscs that separate between the first mixing chamber and the next, aswell as the sizes of the respective apertures.

The 2^(nd) pair of discs are both rotating. In opposite directions.Their speed and the design of their apertures will affect the degree ofmixing effected by the apparatus. The relative speeds of the counterrotating pair of discs is adjusted to determine the sequence oflocations in the chamber where the flow continues to the next chamber(where another pair of counter rotating discs is fitted, or for the lastchamber the flow goes out of the mixer).

The holes of the counter rotating discs are of same size and shape andthey are both situated on the disk so that when the discs counter rotatethere is an instant of time where the holes in the two discs overlap,and the mixture flows through them. Then the discs keep moving inopposite direction and until they meet again they admit no flow throughthem. The first disc will be rotating at an angular speed w₁, and thesecond disk will be rotating at angular speed w₂, such that w₂=k w₁,where k is the configuration coefficient. If we take time point t=0 as astarting point where the two counter rotating discs overlap with theirrespective holes, and we wish for a period T to be marked before theholes overlap again, then we can write:T(w ₁ +w ₂)=2π

And modify it to: T(w₁+kw₁)=2π which leads to w₁=2π/(T(1+k)) andw₂=2πk/(T(1+k)).

If k=1 w₁=w₂=π/T and in that case the next overlap will be exactlyopposite the location where the starting overlap took place. For k=2 thenext overlap will happen 120 degrees away from the former overlap, andso on 120 degrees apart. For k=3 the next overlap will happen π/4 (90degrees) apart. This sequence of locations and the period T, has astrong impact on the resulting uniformity of the mixture. The speed andaperture sizes of the counter rotating discs separating every mixingchamber in the EMA are all mixing parameters.

Entropic Reading Technology

The basic technology of digital photography is the natural means forentropic reading. Today the resolution is very high so that small areasmay be read with a large number of pixels which will identify A colorversus a B color.

Every superficial reading will do. It may be a naturally emittingradiation, or a stimulated radiation. The radiation frequency may be anyfrequency that can be reliably measured. There is a need to distinguishbetween two frequencies to distinguish between A and B. Similarly thephotoelectric effect can be used to distinguish between A and B by theirphotoelectric response to a given radiation frequency.

Photographic entropic reading is not affected by the relativedisposition of the reader versus the examined surface.

An entropic message may be written robustly so that if the examinedsurface is partially dirty, smeared, covered, the reader may overcomethis disturbance. In fact, a reader may develop a credible estimate asto the accuracy of its reading based on the dirt or smear level ofexamined surface.

Entropic Error Recovery

Entropic reading is robust. If part of the inspected surface is covered,or misread, the entropic message may still be recovered. This applies toletters, words or sentences written in Entropia language. We describeahead two reading errors recover methods: 1. worst case scenario, and 2.most plausible case scenario.

In cases where an error in reading has a critical effect, one will leantowards the worst case scenario where an error recovery is most likelyto be accurate, and in other times the plausible case scenario is moreplausible choice.

Worst Case Error Recovery Method

Consider a mixture M of two ingredients A and B, and consider anentropic reader with a reading resolution that identifies m pixels orreading units on the surface of M. a of these pixels are color A, b ofthese pixels are colored B, but u pixels are unidentified, as to whetherthey are colored A or B. This is because these pixels are covered,smeared, dirty, etc. Using any selected method one reads M as if the upixels are either all A or either all B.

One first assumes that every unidentified pixel is an A pixel. Based onthis example the ER evaluates the entropic message E_(a) of M. Next oneassumes that every unidentified pixel is a B pixel, and accordinglyevaluates the entropic message of M—E_(b).

In the case that E_(a)=E_(b), the ER assumes that this is the correctreading of mixture M. That is because it stays the same message in bothextreme cases where all unidentified pixels are marked all in one color.The confidence in having the right reading is high.

Obviously the larger the ratio of u compares to a and b, the more likelyit will be that E_(a)≠E_(b), and in that case the ER will report “unableto read the mixture”.

Plausible Case Error Recovery Method

We repeat the case described in the worst-case scenario. Only that wecolor the unidentified pixels differently. Reading the readable a+bpixels, one computes the ration R_(ab)=a/b. And then randomly assigns Aor B colors to the u unidentified pixels such that a′ of these pixelsare marked color A and b′ of these u pixels are marked color B, and a′and b′ maintains the ratio: R_(ab)=a′/b′. Once so marked the ERdetermines the entropic message of M: E₁.

The above procedure of randomly marking the u unidentified pixels isthen repeated t times. Each time the entropic message E is evaluated.This yields a series of measurements: E₁, E₂, . . . E_(t)

One then sets an a-priori confidence level, CL: 0≤CL≤1. If a count oft*CL entropic messages are the same message, then this message is theplausible reading of M. If there is no t*CL count of cases that agree onthe same message then the ER announces the mixture M as unreadable.

Alternatively, the ER may retry the above method over a lower confidencelevel CL′<CL.

As a matter of protocol the ER may keep lowering the confidence leveluntil it evaluates to a reading, which is then reported along with theconfidence level associated with it.

Of course, the larger the number of rounds (large t) the more reliablethe method.

The Entropic Photoelectric Effect

Entropic message can be established by mixing two chemical elements Aand B such that they are distinguishable by their photoelectricproperties. Let T be a threshold electromagnetic radiation such thatwhen T is projected upon A, it triggers the photoelectric effect, namelyA release electrons which may be attracted to a near by positiveelectrode and register an electrical current. However when radiation Tis projected on element B, it does not have a sufficiently highfrequency to release electrons from B, so no current will be registered.A device that glides above a mixture of A and B will be able to map themixture as to its entropic properties.

The photoelectric mixture as described may be comprised of elements ofsimilar color, so the messaging may not be very visible.

Entropia—Applications

We discuss:

1. material identity verification 2. communication technology 3. visualalert 4. Tactile and dark applications

Material Identity Verification

This application relates to shipping, material authenticity (preventingfraud), material handling (preventing errors and mistakes).

Advantages: robustness of accurate reading, adjusting error risk.

Adjusting Error Risk

A message M may be comprised of an important part M_(i) and a lessimportant part M_(l). Using entropic language, M can be written suchthat M_(i) is expressed on a larger mixture, and M_(l) on a smallermixture. Same for several level of importance. Thereby the chance ofmisreading M_(i) is lower than the chance of misreading M_(l).

Categories:

1. Shipping Applications 2. Automated Assembly and Handling 3. Humantracking 4. Vehicle Tracking.

Shipping Applications

Items in shipping are put together in different modes and order. Ifidentity is marked by a shape based alphabet as a label, then it may bethat the label is not accessible, covered, and dirtied up. The shapelessmessage will be readable from any direction, even if some of the surfaceis covered up.

Automated Assembly and Handling

Items rolling on an assembly line, are rotated and swiveled so thatshape based labeling may be hard to read. When items are piled up adifferent surface is visible for each package. Shapeless has anadvantage. Piles of lumber and other items on construction site may becovered with ‘shapeless’ labels readable from a surveying helicopter.

Human Tracking

People can wear hats, helmets, bandanas, and sleeve cuffs shapelesslymarked so they can be tracked via CCTV or flying camera even in a bigcrowd.

Vehicle Tracking

Entropic roofs or entropic blankets may be shapelessly marked andsurveyed from the air or from a bridge, etc.

Mail Sorting

The challenge of a mail system is that packages and envelopes aregleaned from dispatch locations and must be sorted first on bigcategories of destination and then to more refined definitions ofdestinations. In the normal way an address is written this is not easyto do. Using Shapeless, the big categories of destination—destinationzones—will be entropically marked on the package for quick sorting,followed later by refined sorting for delivery.

Entropic Communication Technology

The entropic alphabet can be used to ‘paint surfaces’ with a message,that is subsequently read by a proper reader, which may be a simpledigital camera. The competition for entropic messaging is (i) nominalalphabet, and (ii) bar codes and QR.

Both nominal alphabet and QR are more efficient with respect toinformation density per surface area. Hence both are nominally muchpreferred to Entropia. Alas, Entropia may be used in a cryptographiccontext, and it has an advantage in situations when readability isdisturbed, or is done from awkward position. Entropia can also be usedin combination with other languages, either next to each other or inoverlap.

Entropia can be written on curved and wavy, or even folded surfaces, forwhich its competition is intolerant.

The basic configuration for Entropia communication is: an entropicwriter painting a display board (normally a computer screen), a cameracapturing the screen, feeding the captured screen into an entropicreader, which interprets and outputs the message prepared by theentropic writer.

Entropic Screen Construction

Unlike the task of embedding an entropic message into a lump of matter,screen construction is more straight forward. One first decides on thedesired entropic message E(R,U)—the ratio level, and the uniformitylevel. One then decides on the size of the display, D, (the equivalentto the M value in the material verification version). D=M is decided interms of its pixel size, say m=pq pixels, for a rectangular withdimensions p and q. It is important that m is adjusted so that there isa solution for the following equation: R=x/(m−x)

If one then marks D with a=x pixels with color A, and b=m−a pixels withcolor B, then the A-B ratio on D will be the desired value R.

The question now is how to distribute the a A color pixel and the b Bcolor pixels. We assume without losing generality that a≤b.

The maximum uniformity over D with R will be when every A pixel isadjacent to only B pixels: U_(max). The smallest uniformity will be whenall the a A pixels are in maximum adjacency, one rectangular block allof A pixels: U_(max).

The values of U_(min), and U_(max) depend on the chosen size of theslice S. The ‘uniformity span’ ΔU=U_(max)−U_(min) is higher for largerslice S, and is highest for the case where the slice fits display.ΔU→ΔU_(max) for |S|→|D| And also dΔU/d|S|>0

One needs to choose a slice S such that the desired uniformity value ofthe message U=U_(m) will be within the limits:U_(min)(S)≤U_(m)≤U_(max)(S)

Now the the challenge is to find the distribution of pixels that will beread as uniformity U_(m).

There are analytic solutions to this challenge that can be programmed tothe entropic message writer. But it can also be accomplished with trialand error.

The entropic message writer, starting from either side, say from the lowuniformity side: will put a block of a A pixels somewhere, and thenapply the standard differential analysis to read the uniformity of thedisplay. If the read uniformity, U_(r) is smaller than the desireduniformity U_(m) then one will choose some method to randomly breakapart some contiguous A pixels and re-read the resultant uniformity. Ifthe read uniformity U_(r) is higher than the desired uniformity U_(m),then one will randomly attach some disjoint blocks of A pixels, andmeasure the resultant uniformity. The message writer thereby has meansto affect both the increase of the uniformity reading and its decrease.By applying these two means in a feedback cycle, then over someadjusting rounds the message writer will achieve the desired uniformityreading on the screen. U_(r)=U_(m).

After some time the entropic writer will have a database for blocksizing for various desired entropic messages.

Superimposing Shape and Shapeless Alphabet

Consider a screen carrying a shape-based message written say in Latinletters.

The letters are marked with a dark color, “ink”, and the background, the“page,” is marked with a light color. The same size screen with the samenumber of pixels may be entropically marked via two colors A and B. Eachof the ‘shapeless’ pixels will be marked by a color for A or a color forB. So we have one ‘shape based’ screen and an equal size ‘shapeless’screen. One shape based message, and one entropic shapeless message. Ifthe two screens are superimposed then each pixel will be marked by oneof the four combinations: A-ink, A-page, B-ink, B-page. One can now usetwo distinct shades of light background colors, L₁ and L₂, such that ahuman reader will not distinguish between them. And one could furtheruse two shades of dark ink colors, D₁, D₂ so that a human reader willnot distinguish between them.

To affect the superimposition one will mark each background “page” pixelon the shape-based screen as L₁ if that pixel is marked as A color onthe entropic screen, and will mark every “page” pixel on the shape basedscreen as L₂, if that pixel is marked as color B on the entropic screen.

One will also mark every “ink” pixel on the shape based screen withshade D₁ if that pixel is marked as color A on the entropic screen. Andevery “ink” pixel on the shape based screen that is marked as color B onthe entropic screen will be marked as D₂.

This superimposition will allow the human reader, or a camera thatsimulates human reading, to read the shape-based message clearly becausethe distinction between L₁ and L₂, as well as the distinction between D₁and D₂ will not be discerned by the human reader.

The same superimposed screen will be readable by a camera that doesdistinguish between L₁ and L₂, as well as between D₁, and D₂. Thatdistinguishing camera will interpret all pixels marked as L₁ or as D₁ ascolor A and interpret every pixel marked as L₂ or D₂ as color B. Thatcamera will then feed a computing machine that will read the entropicmessage of the screen.

As described, except for limitation on size of messages, everysuperimposed screen can carry two arbitrary messages, one through theshape-based interpretation of the superimposed screen and one throughthe shapeless based interpretation thereto.

This superimposition can be enhanced by allowing some/shades of light:L₁, L₂, . . . L_(l) and d shades of dark: D₁, D₂, . . . D_(d) to beused. The human reader will not distinguish between the shades andcomfortably read the shape based message on the screen but the entropicreader will read several bilateral entropic messages on the same screen.

The multiplicity of shades can be used to add boundaries, say a fencecolor F to mark the boundary of a screen slice used to express anentropic letter through colors A and B. The F color can be used tocombine letters to words, and words to phrases etc. All in asuperimposed way relative to the shape based message. There is room foroptimization. If one desires to write a message M on a given screen SCusing colors A and B for the lettering, and using a fencing color F tobound letters and put them next to each other to form words, then thesize of the boundaries, as well as the size of the alphabets is subjectto optimization.

The entropic message superimposed on the shape based message can be asignature S computed by a unique key of the writer, K: M=f(M*, K) whereM* is the shape-based message of the superimposed screen. M will then bewritten on the same screen. f may represent encryption or a hash.

A reader aware of the key K used by the writer will read the shape basedmessage M*, compute M=f(M*,K), and check if the computation matches theM message read entropically on the screen. This will assure the readerthat the shape-based message is authentic, written by the writer whoowns key K. This signature may take any symmetric cipher as its base. Itcan also be used in an asymmetric setting where the writer of the shapebased message, M*, will use a private key K_(pr) to encrypt M* to Mwhile the reader will use the public key of the writer K_(pu) to computeM* from M and check that the computation and the identified M messageagree. If they do, then the reader develops confidence in theauthenticity of the shape based message.

Cryptographic Applications

The cryptographic applications of Entropia have several aspects. Firstthe code book that interprets entropic values may be a shared secret.Second, the size of the slice may be a shared secret. Different slicesizes yield different entropic readings, and the size of the slice isnot given in the display or on the mixture. Third aspect relates tomulti component Entrpoia, where the attacker does not know what is thebilateral combination that is to be read, among the many possibilities.

Inherently the same message delivered entropically several times isdelivered differently every time. Making it difficult to practice chosenplaintext attack.

The shape of a shapeless message may be used as subliminal languageattached to the entropic message, or alternatively the shapeless messagecan be regarded as a subliminal message relative to the shape-basedmessage. The association between these two types of messages opens thisprocedure to many of the applications of such message association, likethe applications identified in U.S. patent Ser. No. 10/395,053.

The entropic message may be written randomly as shown above, so everyone who writes it will generate a different picture (shape).

Bit Wise Entropia

A square of w*w bits will allow for I_(r)=w²−1 letters based on ratioonly. Adding uniformity will greatly increase the size of the alphabetassociated with this square. If the entropic message is read throughrandom slices, say of size 16 bits, then even the simple case whereingredient A is one bit and ingredient B the other 15 bits, will havethree or more entropic message. Placing the A bit in the middle of thesquare or close to it, will yield a different uniformity reading whencompared to placing the A bit at the corner of the square or at itsside.

Illustration: the uniformity of case I is different from the uniformityof case II and Case III below.

Case 1: entropic mixture M is 3*3 squares (w=3) with ratio R=1/8. The Aingredient, marked as ‘1’ is placed in the middle, and the ingredientB—zeros are placed around:

$\begin{matrix}0 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 0\end{matrix}$

Case II—as above but the mapping is as follows:

$\begin{matrix}0 & 0 & 1 \\0 & 0 & 0 \\0 & 0 & 0\end{matrix}$

Case III: as above with mapping as follows:

$\begin{matrix}0 & 0 & 0 \\0 & 0 & 1 \\0 & 0 & 0\end{matrix}$

For slices of size 2 bits and above. For slices of size one bit, thethree above cases will yield the same uniformity reading (and hence thesame entropic reading because the ratio is the same). And for a slicethe size of M (3*3) also the reading is the same. But for square slices,say of the form (size 4 bits):

$\begin{matrix}X & X \\X & X\end{matrix}$

Case 1 will catch the A bits more times because it is in the middle.There are 4 possible slice of size 2×2 bits square. All four of themwill catch the A bit. Alas only one of the four slices will catch A inCase II, and two slice will catch A in Case III. Therefore the entropicmessage of the three cases will be different.

Specifically, a 2×2 slice without A (all 4 bits are B) will have thefollowing uniformities:

Case I: Each slice contains 3 B and 1 A. ComputingR₄=(3+3+3+3)/(1+1+1+1)=3. NowU=1−(1/(1/4*3*4))((1*4−4)+(1*4−4)+(1*4−4)+(1*4−4))=1.00

Case II. One slice contains 1 A and 3 B, and the three other slices areall B. Hence R₄=(4+4+4+3)/(0+0+0+1)=15. Computing:U=1−(1/(4*15*4))((4−0)+(4−0)+(4−0)+|(3−1*15)|)=0.90

Case III: two slices contain 1 A, two slices contain no A. ComputingR₄=(4+4+3+3)/(0+0+1+1)=7. Computing:U=1−(1/(4*7*4))((4−0)+(4−0)+|(3−1*7)|+|(3−1*7)|)=0.86

The above illustration points out that for a bit-wise mixture of size pbits over q bits, using the differential method, any sequence of the2^(pq) combinations will be associated with an Entropic letter definedover a well defined set of slices, say a slice of p′ bits over q′ bits.One would simply evaluate all the possible slices of p′×q′ size, and usethe differential formula to compute R and U as in the illustrationabove, and from these values identify the entropic message—the entropicletter. This will map bit matrices of any size to a uniformity number0≤U≤1. It will identify matrices of size p×q sharing the same uniformityand entropic letters. This determinism in computing entropic messagegives rise to various cryptographic protocols.

Visual Alert

A tool to notice changes of interest in a monitoring video camera. Inmany situations today a large number of CCTV cameras are trained onpublic places, or military targets as the case may be. There aregenerally not enough people to keep watch of these TV cameras. There arealso not enough AI processors to apply serious inference enginesoperation on the video stream. This situation may be helped withEntropia.

As the video is displayed, it is constantly analyzed by an entropicreader. Reading does not have to be accurate, it has to be fast. Theentropic camera may sample frequent frames in the video stream, andanalyze them. As soon as the analysis is complete the entropic camerasamples another frame in the video stream. If the entropic message ofthe screen undergoes a great change, especially if sudden, then thisvideo is becoming of interest. Case in point: dozens of CCTV around aplant are surveying what is in front of them. Nothing much happensnormally, and a human surveyor cannot be expected to pay much attention.When normal workers go back and forth in the surveyed area, the picturechanges, but the entropic message stays very much the same. However,suppose that fire erupts in some location. The CCTV camera video will beentropically analyzed and a big change will be noticed, so that videostream will be sent for a human evaluator to analyze. This entropicsurveillance will also work if someone quickly opens a lock door andgets in. The movement of the person and the opened door will beregistered as an entropic change of interest. The implementer willdecide on the threshold of change to be reported.

Once a camera is recognized as warranting interest, it can be submittedto human monitoring for human analysis. In a larger arrangement, theremay be a small number of highly powerful AI engines which can analyzeonly a small fraction of the total number of CCTV cameras. In that case,any camera that was triggered by Entropic alert will be forwarded forfurther analysis at AI grades.

What is the advantage of Entropia?

A video camera, trained on a public place, or other certain places,shows people coming and going, trees blowing in the wind, birds flyinganimal walk by, cars, clouds, rain, etc. Such innocent changes to thevideo picture are of no special interest. But if fire breaks out, aflood happens, someone scales a wall, or cuts a wire, a crowd walksin—these are changes that need attention. It is therefore important todifferentiate between normal video dynamics and abnormal dynamics whereattention is needed. Today there are anticipatory algorithms for thatpurpose. They are programmed to recognize a fire, or a crowd forexample. But anticipatory algorithms cannot anticipate what a creativeattacker will do. The Entropic solution is to constantly monitor theentropic message of the video. A moving cloud, a flying bird, paperflying in the wind, etc., will not modify the entropic reading a video.But a fire, a flood, a big crowd will be evaluated to a differententropic reading, and trigger the alert.

It is clear that it is not necessary to measure the entropic messageaccurately, because only the dynamics is of interest.

The entropic reading can be done over black v. white, red v. blue, greenv. yellow, etc. or any combination thereto.

Tactile and Dark Applications

Nominal Reading in dark environments is impossible. A tactile solutionis called for. While it is possible to read shape-based alphabet withhuman or machine touch (Braille alphabet), it is error prone, on accountof position and orientation. By contrast shapeless alphabet is much moreconducive to dark reading.

A surface may be marked with smooth section (ingredient A) and roughsections (ingredient B), a tactile apparatus feeling itself on thesurface at a known speed with say randomized direction of movement, willread A areas versus B areas, and interpret the shapeless message of theinspected surface.

Roughness gradient of surfaces may also be used for reading throughmeasuring returned light from a light projector (or any other properlydistinguished electromagnetic radiation).

Roughness may be set in various identified degrees, and thereby use thetactile format for multi component entropic messaging.

Rock of Randomness

U.S. Pat. No. 10,467,522 describes a “rock of randomness” comprised ofsome n constituents marked with diverse electrical resistance. The ideabehind the rock is that these constituents should be randomly mixed butnot at high uniformity. The rock describes a 3D printing technique toconstruct such a rock of randomness. This invention offers anothertechnology for that purpose. An entropic mixer apparatus could be set tomix the required n constituents in the desired way. This will be anapplication of the physical apparatus for other than writing an entropicmessage.

Human Reading

The human eye will naturally distinguish between sufficiently differententropic letters. Which suggests a ‘reduced entropic language’ reliablyreadable by just looking. There are countless applications where signalsare important in some complex situations, perhaps of emergency andrescue. We normally use colored flags to communicate basic messages.E.g. red and white flags on a beach. We indicate a ‘country’ by itsparticular flag. The entropic concept will simply push thiscommunication channel further. Parameters are: the choice of the pair ofcolors to look at, the ratio of the quantities between these colors, andthe uniformity of the mix. The human eye can easily distinguish betweentwo colors in three ratio modes: 90%:10%, 50%:50%, 10%:90%. The humaneye can also easily distinguish between three uniformity modes: (i)isolated large blocks for each color, (ii) small size isolated blocksfor each color, and (iii) a thorough mixture of the two colors. Testsmay indicate that the human eye is more sensitive than that. When theratio is very much off (one colors dominates) uniformity distinction ismore difficult than when the two colors are roughly equal, but all inall it looks like an alphabet of 9 letters is a practical arrangement.Hence a flag that is comprised of three patches, each showing anentropic letter through a different pair of colors (e.g. red-blue,green-black, yellow-grey), will be able to display words comprised of 3letters, from an alphabet of 9 letters: 9³=729 distinct messages. Thisis sufficiently rich to convey critical information in an emergency.There is a good chance that with some training people will be able toread much richer entropic messages with no camera aid, just by looking.

Overview of the Invented Technology

1. This invention describes a method to express information with analphabet that is not based on shapes, forms, and fixed geometry of itsletters, a “shapeless alphabet”, by mixing two ingredients A and B intoa mixture M, wherein the ratio between the ingredients, and theuniformity of the mixture together express a letter of the shapelessalphabet, and where the ratio between the ingredients, R is defined asthe R=Q_(a)/Q_(b), where Q_(a) an Q_(b) are the quantities ofingredients A and B respectively, such that Q_(m) is the quantity of themixture M, where Q_(m)=Q_(a)+Q_(b), and where the uniformity of M ismeasured relative to slices S₁, S₂, . . . S_(n) marked randomly on M,such that their sizes are all the same, Q_(s), and equal to Q_(s)≤Q_(m),and the uniformity of the quantitative ratios between ingredients A andB in the n slices, R_(i)=Q_(ai)/Q_(bi), for i=1, 2, . . . n, for n→∞,expresses the uniformity, U, of the mixture M, and where the shapelessalphabet letter, L, that is expressed by M is a function of R and U:L=f(R,U).

2. This invention describes a system to mix two viscous incompressiblechemical ingredients A and B to create a mixture M such that the ratio Rbetween the volume of A, V_(a), and the volume of b, V_(b) in M is agiven ratio, and such that the uniformity of the mixture M is of desiredvalue, U, where U is defined as follows: (i) one randomly marks n sliceson M where all the slices are of volume V_(s)≤V_(m), where V_(m) is thevolume of M, then (ii) one measures the n ratios between ingredients Aand B in each of the n slices, and uses a certain established uniformitycalculating formula to compute the uniformity U of M, from the n ratiovalues, for a pre-established value of n.

3. This invention describes a system to create a surface M, comprised ofsmooth area, A, and rough and uneven area B, where the ratio between thesurface size of the smooth patches, P_(a), and the surface size of therough patches, P_(b), is an arbitrary value R=P_(a)/P_(b), and where theuniformity between the smooth and the rough patches, is an arbitraryvalue U, where U is defined as follows: (i) one randomly marks n sectorson M where all the sectors are of area A_(s)≤A_(m), where A_(m) is thearea of M, then (ii) one measures the n ratios between patches of A andpatches of B in each of the n sectors, and uses a certain establisheduniformity calculating formula to compute the uniformity U of M, fromthe n ratio values, for a pre-established value of n.

4. This invention describes a method as in (1) wherein the uniformity Uof M is computed via the following formula:U=1−(1/(Q _(s) *R _(n) *n))Σ|R _(n) Q _(ai) −Q _(bi)| . . . for i=1,2, .. . nwhere:R _(n) =ΣQ _(ai) /ΣQ _(bi) . . . for i=1,2, . . . n

and R=R_(n).

5. This invention describes a method as in (1) wherein the ingredients Aand B are incompressible viscous fluids, with no mutual chemicalreaction, and where the mixture M is either a viscous fluid or a solidconstruction; and where the quantities of ingredients A and B aremeasured as volumes, and where the slices may be arbitrary parts of themixture, or they may be thin slices, namely having one spatial dimensionvery small, or they may be line-type slices, having two spatialdimensions very small.

6. This invention describes a method as (1) wherein t>2 ingredients I₁,I₂, . . . I_(t) are mixed into a mixture M, such that any twoingredients i and j, i, j=1, 2, . . . t define a Shapeless letterL_(ij)=f(R_(ij), U_(ij)), where R_(ij), and U_(ij) are the entropicratios and entropic uniformities defined over ingredients I_(i), andI_(j), and where any set of the t ingredients, α, may be regarded as asingle ingredient A, while any set of the t ingredients, β, may beregarded as a single ingredient B, such that when sets α and β aremutually exclusive, these two sets will define an entropic letterL_(αβ)=f(R_(αβ), U_(αβ)), where R_(αβ) and U_(αβ) are the ratio anduniformity for α, and β.

7. This invention describes a method as in (1) where the A, Bingredients are superficial areas marked on a computer screen, which areset dynamically by a computing machine that expresses an arbitrarymessage T by writing successive entropic letters L₁, L₂, . . . on thescreen, and where the screen is captured by one or more cameras eachsending the screen picture into a reading computing machine, whichinterprets the entropic letters L₁, L₂, . . . into T.

8. This invention describes a method as in (1) where a pair of colors ina video stream are regarded as ingredients A and B, such that each frameof the video stream may be regarded as a mixture M_(video) comprised ofcolors A and B and all other colors, which are neither A nor B such thatevery frame F_(i) of the video stream may be interpreted as carrying anentropic letter L_(i) defined by the ingredients A and B, resulting inthe video projecting a message comprised of letters L₁, L₂, . . . .

9. This invention describes a system in (2) where the mixture M iscreated via an apparatus comprised of an “entropic mixer”, EM that mixesingredients A and B into a mixture stream M, which in turn is read by an“entropic reader” ER to determine the entropic letter L written into M,and where this reading is communicated to an entropic controller, EC,which compares the reading, L, to a set point value, L_(sp) given to it,and then the EC adjusts operational parameters in the EM in order togenerate M with the desired set point letter L_(sp), the adjustedmixture stream M is again read by the ER that evaluates its entropicletter L′, and communicates L′ to the EC, which again adjusts theoperational parameters of EM until L_(sp)=L_(m), where L_(m) is theletter written on M when the feedback control sequence is completed.

10. This invention describes a system in (9) where the EM is comprisedof two feeding lines for ingredients A and B such that the EC controlsthe flow rates of A and B, and where the feed lines terminate in a firstcontraption comprised of two discs mounted perpendicular to the flow ofthe ingredients, fitting snugly into the flow pipe for A and B, andwhere one disc is stationary, and one disc is rotating at a speedcontrolled by the EC, and where the stationary disc is drilled withholes of a set size, one hole allowing ingredient A to flow through andone hole allowing ingredient B to flow through, and where the rotatingdisc, rotates abreast and next to the stationary disc, and it has asingle hole drilled into it, such that when this rotating hole overlapswith the hole for A in the stationary disc, ingredient A flows through,and when this rotating hole overlaps the hole for B in the stationarydisc, ingredient B flows through, and where the alternatingdisc-flow-through quantities of A and B that flow beyond the first twodisc contraption, keep flowing to a second two disc contraption whichare perpendicular to the flow of ingredients A and B, and which fitsnugly into the flow pipe, and where the two discs rotate in oppositedirections, and each has a hole in it, and when the two holes overlapthe mixture of A and B flows through; the flow then meets another one ormore two disc contraptions of the second type, and after the last twodisc contraption the mixture is let outside from the EM; the holes inthe various discs may be changed and controlled by the EC, so is thespeed of rotation of every disc in the contraption, such control is usedto generate a mixture M associated with letter L_(m) which is the sameas the desired, set point L_(sp)=L_(m)

11. This invention describes a system as in (3) where a surface isevaluated via an entropic reader projecting a laser beam onto thesurface at an angle α off the perpendicular of the surface, where asmooth area on the surface reflects the beam with another beam of thesame angle α, such that the two beams mark an angle 2α between them,while a rough area of the surface will scatter the incoming beam, andwhere the entropic reader will measure the amount of radiation reflectedat angle α, and thereby determine if the evaluated spot is smooth(ingredient A), or rough (ingredient B), the projected beam and thereflection reader are mounted on a structure that moves above theexamined surface and thereby maps the entropic state of the surface withrespect to A and B.

12. This invention describes a system as in (3) where establishedmetrics of roughness and smoothness are used to mark a surface with tdistinct states of roughness-smoothness, such that any two such statescan define an entropic message over the surface where the smooth andrough spots are marked.

13. This invention describes a method as in (1) where a first screen Scomprised of p×q pixels is set to express a shape-based letter like aletter from the Latin alphabet by coloring some g<pq pixels with a lightcolor, to serve as the “page”, the background, and coloring the otherpq−g pixels with a dark color, “ink”, such that the shape marked by theink surrounded by the page, displays a visual letter, or several lettersfrom the Latin alphabet, and where a second screen of same size is usedto express an entropic message as in claim 1 by marking a pixels asingredient A for the bilateral entropic message, and b=pq−a pixels asingredient B for the bilateral entropic message, and where the first andthe second screens are superimposed by the use of two shades of lightcolor: L₁ and L₂, as well as two shades of dark color, D₁, and D₂ suchthat a human reader of the screen will not distinguish between L₁ andL₂, and also not distinguish between D₁ and D₂, but a special sensitivecamera will distinguish between L₁ and L₂, and distinguish between D₁and D₂, the superimposition will proceed by marking every page pixelwhich the second screen marked as color A to be colored with shade L₁,and every page pixel which the second screen marked as color B to becolored with shade L₂, and marking every ink pixel which the secondscreen marked as color A to be colored with shade D₁, and every inkpixel which the second screen marked as color B to be colored with shadeD₂, thereby allowing a human reader to read in the superimposed screenthe message expressed in the first screen, while allowing a sensitivecamera to read in the superimposed screen the message expressed in thesecond screen.

14. This invention describes a method as in (1) where the mixture iscomprised of two ingredients A and B that are distinct chemical elementssuch that a certain “threshold” electromagnetic radiation, T, whenprojected on element A will trigger the photoelectric effect, such thata near by positive pole will attract the released electrons and anelectrical current will be registered, while element B will remainbonded to its electrons and not release them when projected withradiation T, and where an apparatus that projects radiation T on themixture will be gliding at a known speed over the mixture M, and wherethe apparatus will be equipped with electronic circuitry and measure ateach position of M whether an electric current is registered or not, sothat by mapping the locations where current was registered and wherecurrent was not registered, the apparatus will read the entropic messageon M as described in (1).

What is claimed is:
 1. A method to mark packages, and surfaces, withmarkings that are properly readable under conditions wheregeometry-specific markings are not very readable, as on a surface of awaving flag, a surface of a wrinkled package, or of a curved shape, orpartly soiled, by using an alphabet that is not based ongeometry-specific shapes of its letters, rather a “shapeless alphabet”,defined through “shapeless letters” comprising: painting a surface witha sequence of shapeless letters L1, L2, . . . , Lt where each shapelessletter corresponds to a painted area: M1, M2, . . . , Mt where eachpainted area M is a mixture of two distinct colors A and B, such thatQ_(m)=Q_(a)+Q_(b), where Q_(m) is the area of M, and Q_(a) and Q_(b) arethe areas of colors A and B respectively, and where the quantitativeratio between the colors comprising the painted area is computed asR_(m)=Q_(a)/Q_(b), and where the uniformity of M is measured relative toslices S₁, S₂, . . . S_(n) marked randomly on the painted surface, M,such that their areas are all the same, Q_(s), where Q_(s)<Q_(m), andwhere the uniformity of the quantitative ratios between colors A and Bin the n slices, R_(i)=Q_(ai)/Q_(bi), for i=1, 2, . . . n, for anarbitrary large n, expresses the uniformity, U, of the mixture M, andwhere the values of R and U in combination determine the identity of theshapeless letter L, expressed by area M: L=f(U,R).
 2. The method inclaim 1 wherein the ratio R, and the uniformity U of M is computed viathe following formula:U=1−(1/(Q _(s) *R _(n) *n))Σ|R _(n) Q _(ai) −Q _(bi)| . . . for i=1,2, .. . nwhere:R _(n) =ΣQ _(ai) /ΣQ _(bi) . . . for i=1,2, . . . n and where R is setas R=R_(n).
 3. The method of claim 1 wherein t>2 ingredients I₁, I₂, . .. I_(t) are mixed into a mixture M, such that any two ingredients i andj, i, j=1, 2, . . . t define a shapeless letter L_(ij)=f(R_(ij),U_(ij)), where R_(ij), and U_(ij) are the entropic ratios and entropicuniformities defined over ingredients I_(i), and I_(j), and where anyset of the s ingredients, α, may be regarded as a single ingredient A,while any set of the t ingredients, β, may be regarded as a singleingredient B, such that when sets α and β are mutually exclusive, thesetwo sets will define an entropic letter L_(αβ)=f(R_(αβ), U_(αβ)), whereR_(αβ) and U_(αβ) are the ratio and uniformity for α, and β.
 4. Themethod in claim 1 where a first computing device marks a shapelessletter L on a computer screen, and where the two ingredients A and B areof different colors, and where the image thereto is then captured by adigital camera feeding a second computing device which then evaluatesthe captured screen as the shapeless letter written by the firstcomputing device, and where the first computing device then marksanother shapeless letter L′ on its computing screen, and the imagethereto is then captured by the digital camera feeding the secondcomputing device, which then evaluates the second letter L′, and so on,the first computing device passes to the second computing device amessage of arbitrary length by communicating one shapeless letter at atime.
 5. The method in claim 1 where a pair of colors in a video streamare regarded as ingredients A and B, such that each frame of the videostream may be regarded as a mixture M_(video) comprised of colors A andB and all other colors, which are neither A nor B such that every frameF_(i) of the video stream may be interpreted as carrying an entropicletter L_(i) defined by the ingredients A and B, resulting in the videoprojecting a message comprised of letters L₁, L₂, . . . L_(r).
 6. Amethod as in claim 1 where a first screen S comprised of p×q pixels isset to express a shape-based letter like a letter from the Latinalphabet by coloring some g<pq pixels with a light color, to serve asthe “page”, the background, and coloring the other pq−g pixels with adark color, “ink”, such that the shape marked by the ink surrounded bythe page, displays a visual letter, or several letters from the Latinalphabet, and where a second screen of same size is used to express anentropic message as in claim 1 by marking a pixels as ingredient A forthe bilateral entropic message, and b=pq−a pixels as ingredient B forthe bilateral entropic message, and where the first and the secondscreens are superimposed by the use of two shades of light color: L₁ andL₂, as well as two shades of dark color, D₁, and D₂ such that a humanreader of the screen will not distinguish between L₁ and L₂, and alsonot distinguish between D₁ and D₂, but a special sensitive camera willdistinguish between L₁ and L₂, and distinguish between D₁ and D₂, thesuperimposition will proceed by marking every page pixel which in thesecond screen is marked as color A to be colored with shade L₁, andevery page pixel which the second screen marked as color B to be coloredwith shade L₂, and marking every ink pixel which the second screenmarked as color A to be colored with shade D₁, and every ink pixel whichthe second screen marked as color B to be colored with shade D₂, therebyallowing a human reader to read in the superimposed screen as themessage expressed in the first screen, while allowing a sensitive camerato read in the superimposed screen the message expressed in the secondscreen.
 7. A method as in claim 1 where the mixture is comprised of twoingredients A and B that are distinct chemical elements such that acertain “threshold” electromagnetic radiation, T, when projected onelement A will trigger the photoelectric effect, such that a near bypositive pole will attract the released electrons and an electricalcurrent will be registered, while element B will remain bonded to itselectrons and not release them when projected with radiation T, andwhere an apparatus that projects radiation T on the mixture will begliding at a known speed over the mixture M, and where the apparatuswill be equipped with electronic circuitry and measure at each positionof M whether an electric current is registered or not, so that bymapping the locations where current was registered and where current wasnot registered, the apparatus will read the entropic message on M asdescribed in claim
 1. 8. A system to mix two viscous incompressiblechemical ingredients A and B to create a mixture, lump, M, where Mexpresses a shapeless letter L from a given shapeless alphabet,comprising: an “entropic mixer”, EM, that mixes ingredients A and B intoa mixture stream M, which in turn is read by an “entropic reader” ER todetermine the shapeless letter L written into M, an entropic controller,EC, which compares the reading of the shapeless letter, L, to a setpoint letter, L_(sp) given to it, and then the EC adjusts operationalparameters in the EM in order to generate M with the desired set pointletter L_(sp), the adjusted mixture stream M is again read by the ERthat evaluates its shapeless letter L′, and communicates the shapelessletter L′ to the EC, which again adjusts the operational parameters ofEM until L_(sp)=L_(m), where L_(m) is the shapeless letter expressed byM when the feedback control sequence is completed, wherein the identityof the shapeless letter L expressed by the lump M is determined asfollows: the lump M is a mixture of two ingredients A and B such thatthe ratio, R, between the volume of A, V_(a), and the volume of b,V_(b), in M is a ratio corresponding to L, and such that the uniformityof M, U, is of the value corresponding to L, where U is defined asfollows: (i) one randomly marks n slices on M where all the slices areof volume V_(s)<V_(m), where V_(m) is the volume of M, then (ii) onemeasures the n ratios between ingredients A and B in each of the nslices, and uses a certain established uniformity calculating formula tocompute the uniformity U of M, from the n ratio values, for apre-established value of n; so manufactured the shapeless letterexpressed by the lump will be readable from any surface of the lump, andfrom any cut thereto, and thereby identify it.
 9. The system of claim 8where the slices are cut so that one spatial dimension is very small,and thus the slices are effectively two dimensional, and also where theslices, are cut so that two spatial dimensions are very small, and theslices are effectively one dimensional.
 10. The system in claim 8 wherethe EM is comprised of two feeding lines for ingredients A and B suchthat the EC controls the flow rates of A and B, and where the feed linesterminate in a first disc contraption comprised of two discs mountedperpendicular to the flow of the ingredients, fitting snugly into theflow pipe that collects the streams A and B, and where one disc isstationary, and one disc is rotating at a speed controlled by the EC,and where the stationary disc is drilled with two holes of a set size,one hole allowing ingredient A to flow through, and one hole allowingingredient B to flow through, and where the rotating disc, rotatesabreast and next to the stationary disc, and it has a single holedrilled into it, such that when this rotating hole overlaps with thehole for A in the stationary disc, ingredient A flows through, and whenthis rotating hole overlaps the hole for B in the stationary disc,ingredient B flows through, and where the mixture flows beyond the firstdisc contraption, through the pipeline until it encounters a second disccontraption comprising two snuggly fit discs which are fittedperpendicular to the flow of the mixture, and where the two discs rotatein opposite directions, and each has a hole in it, and when the twoholes overlap the mixture of A and B flows through; the mixture thenproceeds through the pipe and flows until it meets another disccontraption similar to the disc contraption of the second type, keepsflowing, until it meets another disc contraption of the second type, andso on, and after the last disc contraption the mixture is let outsidefrom the EM; the holes in the various discs may be changed andcontrolled by the EC, so is the speed of rotation of every disc in thecontraptions, such control is used to generate a mixture M associatedwith letter L which is the same as the desired, set point L*=L.
 11. Amachine readable medium having painted surface M to express a shapelessletter L, of a given shapeless alphabet, comprising: a combination ofsmooth areas, A, and unsmooth areas B, where the ratio between thesurface size of all the smooth areas in M, P_(a), and the surface sizeof all the unsmooth areas in M, P_(b), is the ratio value R=P_(a)/P_(b),corresponding to L, and wherein the uniformity between the smooth andthe unsmooth areas is the value U corresponding to L, where U is definedas follows: (i) one randomly marks n sectors on M where all the sectorsare of area P_(s)<P_(m), where P_(m) is the area of M, then (ii) onemeasures the n ratios between the sum of areas of A and the sum of areasof B in each of the n sectors, and uses a certain established uniformitycalculating formula to compute the uniformity U of M, from the n ratiovalues, for a pre-established value of n; so manufactured the surface Mwill express an intrinsic shapeless letter to identify it to itsreaders.
 12. A machine readable medium as in claim 11 where a surface isevaluated via an entropic reader projecting a regular light or laserbeam onto the surface at an angle γ off the perpendicular of thesurface, where a smooth area on the surface reflects the beam withanother beam of the same angle γ, such that the two beams mark an angle2γ between them, while a rough area of the surface will scatter theincoming beam, and where the entropic reader will measure the amount ofradiation reflected at angle 2γ, and thereby determine if the evaluatedspot is smooth (ingredient A), or rough (ingredient B), the projectedbeam and the reflection reader are mounted on a structure that movesabove the examined surface and thereby maps the entropic state of thesurface with respect to A and B.
 13. A machine readable as in claim 11where established metrics of roughness and smoothness are used to mark asurface with t distinct states of roughness-smoothness, such that anytwo such states can define an entropic message over the surface wherethe smooth and rough spots are marked.